Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,5,Mod(47,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.47");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.7750915093\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.15 | ||
Character | \(\chi\) | \(=\) | 230.47 |
Dual form | 230.5.f.a.93.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | − | 2.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 4.47696 | − | 4.47696i | 0.497440 | − | 0.497440i | −0.413200 | − | 0.910640i | \(-0.635589\pi\) |
0.910640 | + | 0.413200i | \(0.135589\pi\) | |||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | −20.9409 | + | 13.6558i | −0.837634 | + | 0.546231i | ||||
\(6\) | −17.9078 | −0.497440 | ||||||||
\(7\) | −15.4160 | − | 15.4160i | −0.314611 | − | 0.314611i | 0.532082 | − | 0.846693i | \(-0.321410\pi\) |
−0.846693 | + | 0.532082i | \(0.821410\pi\) | |||||||
\(8\) | 16.0000 | − | 16.0000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 40.9136i | 0.505106i | ||||||||
\(10\) | 69.1933 | + | 14.5701i | 0.691933 | + | 0.145701i | ||||
\(11\) | 133.641 | 1.10447 | 0.552237 | − | 0.833687i | \(-0.313774\pi\) | ||||
0.552237 | + | 0.833687i | \(0.313774\pi\) | |||||||
\(12\) | 35.8157 | + | 35.8157i | 0.248720 | + | 0.248720i | ||||
\(13\) | −27.8077 | + | 27.8077i | −0.164542 | + | 0.164542i | −0.784576 | − | 0.620033i | \(-0.787119\pi\) |
0.620033 | + | 0.784576i | \(0.287119\pi\) | |||||||
\(14\) | 61.6638i | 0.314611i | ||||||||
\(15\) | −32.6150 | + | 154.888i | −0.144956 | + | 0.688391i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −6.97609 | − | 6.97609i | −0.0241387 | − | 0.0241387i | 0.694934 | − | 0.719073i | \(-0.255433\pi\) |
−0.719073 | + | 0.694934i | \(0.755433\pi\) | |||||||
\(18\) | 81.8272 | − | 81.8272i | 0.252553 | − | 0.252553i | ||||
\(19\) | − | 581.940i | − | 1.61202i | −0.591901 | − | 0.806011i | \(-0.701622\pi\) | ||
0.591901 | − | 0.806011i | \(-0.298378\pi\) | |||||||
\(20\) | −109.246 | − | 167.527i | −0.273116 | − | 0.418817i | ||||
\(21\) | −138.033 | −0.313001 | ||||||||
\(22\) | −267.283 | − | 267.283i | −0.552237 | − | 0.552237i | ||||
\(23\) | −77.9968 | + | 77.9968i | −0.147442 | + | 0.147442i | ||||
\(24\) | − | 143.263i | − | 0.248720i | ||||||
\(25\) | 252.039 | − | 571.928i | 0.403262 | − | 0.915084i | ||||
\(26\) | 111.231 | 0.164542 | ||||||||
\(27\) | 545.803 | + | 545.803i | 0.748700 | + | 0.748700i | ||||
\(28\) | 123.328 | − | 123.328i | 0.157306 | − | 0.157306i | ||||
\(29\) | − | 1422.24i | − | 1.69113i | −0.533871 | − | 0.845566i | \(-0.679263\pi\) | ||
0.533871 | − | 0.845566i | \(-0.320737\pi\) | |||||||
\(30\) | 375.006 | − | 244.546i | 0.416673 | − | 0.271717i | ||||
\(31\) | −109.874 | −0.114333 | −0.0571666 | − | 0.998365i | \(-0.518207\pi\) | ||||
−0.0571666 | + | 0.998365i | \(0.518207\pi\) | |||||||
\(32\) | 128.000 | + | 128.000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 598.307 | − | 598.307i | 0.549409 | − | 0.549409i | ||||
\(34\) | 27.9044i | 0.0241387i | ||||||||
\(35\) | 533.340 | + | 112.306i | 0.435380 | + | 0.0916786i | ||||
\(36\) | −327.309 | −0.252553 | ||||||||
\(37\) | 347.767 | + | 347.767i | 0.254030 | + | 0.254030i | 0.822621 | − | 0.568591i | \(-0.192511\pi\) |
−0.568591 | + | 0.822621i | \(0.692511\pi\) | |||||||
\(38\) | −1163.88 | + | 1163.88i | −0.806011 | + | 0.806011i | ||||
\(39\) | 248.988i | 0.163700i | ||||||||
\(40\) | −116.561 | + | 553.546i | −0.0728507 | + | 0.345966i | ||||
\(41\) | −1500.74 | −0.892764 | −0.446382 | − | 0.894842i | \(-0.647288\pi\) | ||||
−0.446382 | + | 0.894842i | \(0.647288\pi\) | |||||||
\(42\) | 276.067 | + | 276.067i | 0.156500 | + | 0.156500i | ||||
\(43\) | 687.304 | − | 687.304i | 0.371716 | − | 0.371716i | −0.496386 | − | 0.868102i | \(-0.665340\pi\) |
0.868102 | + | 0.496386i | \(0.165340\pi\) | |||||||
\(44\) | 1069.13i | 0.552237i | ||||||||
\(45\) | −558.708 | − | 856.766i | −0.275905 | − | 0.423094i | ||||
\(46\) | 311.987 | 0.147442 | ||||||||
\(47\) | −97.5012 | − | 97.5012i | −0.0441382 | − | 0.0441382i | 0.684693 | − | 0.728831i | \(-0.259936\pi\) |
−0.728831 | + | 0.684693i | \(0.759936\pi\) | |||||||
\(48\) | −286.526 | + | 286.526i | −0.124360 | + | 0.124360i | ||||
\(49\) | − | 1925.70i | − | 0.802040i | ||||||
\(50\) | −1647.93 | + | 639.777i | −0.659173 | + | 0.255911i | ||||
\(51\) | −62.4634 | −0.0240151 | ||||||||
\(52\) | −222.461 | − | 222.461i | −0.0822712 | − | 0.0822712i | ||||
\(53\) | 2457.09 | − | 2457.09i | 0.874722 | − | 0.874722i | −0.118261 | − | 0.992983i | \(-0.537732\pi\) |
0.992983 | + | 0.118261i | \(0.0377319\pi\) | |||||||
\(54\) | − | 2183.21i | − | 0.748700i | ||||||
\(55\) | −2798.56 | + | 1824.98i | −0.925145 | + | 0.603298i | ||||
\(56\) | −493.310 | −0.157306 | ||||||||
\(57\) | −2605.32 | − | 2605.32i | −0.801884 | − | 0.801884i | ||||
\(58\) | −2844.48 | + | 2844.48i | −0.845566 | + | 0.845566i | ||||
\(59\) | − | 3828.70i | − | 1.09989i | −0.835202 | − | 0.549943i | \(-0.814649\pi\) | ||
0.835202 | − | 0.549943i | \(-0.185351\pi\) | |||||||
\(60\) | −1239.10 | − | 260.920i | −0.344195 | − | 0.0724778i | ||||
\(61\) | −5066.25 | −1.36153 | −0.680765 | − | 0.732502i | \(-0.738352\pi\) | ||||
−0.680765 | + | 0.732502i | \(0.738352\pi\) | |||||||
\(62\) | 219.748 | + | 219.748i | 0.0571666 | + | 0.0571666i | ||||
\(63\) | 630.722 | − | 630.722i | 0.158912 | − | 0.158912i | ||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | 202.581 | − | 962.051i | 0.0479481 | − | 0.227704i | ||||
\(66\) | −2393.23 | −0.549409 | ||||||||
\(67\) | 1522.51 | + | 1522.51i | 0.339164 | + | 0.339164i | 0.856052 | − | 0.516889i | \(-0.172910\pi\) |
−0.516889 | + | 0.856052i | \(0.672910\pi\) | |||||||
\(68\) | 55.8087 | − | 55.8087i | 0.0120694 | − | 0.0120694i | ||||
\(69\) | 698.377i | 0.146687i | ||||||||
\(70\) | −842.068 | − | 1291.29i | −0.171851 | − | 0.263529i | ||||
\(71\) | −1397.47 | −0.277221 | −0.138611 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138611 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(72\) | 654.618 | + | 654.618i | 0.126277 | + | 0.126277i | ||||
\(73\) | 1262.48 | − | 1262.48i | 0.236907 | − | 0.236907i | −0.578661 | − | 0.815568i | \(-0.696425\pi\) |
0.815568 | + | 0.578661i | \(0.196425\pi\) | |||||||
\(74\) | − | 1391.07i | − | 0.254030i | ||||||
\(75\) | −1432.13 | − | 3688.87i | −0.254601 | − | 0.655799i | ||||
\(76\) | 4655.52 | 0.806011 | ||||||||
\(77\) | −2060.21 | − | 2060.21i | −0.347480 | − | 0.347480i | ||||
\(78\) | 497.975 | − | 497.975i | 0.0818500 | − | 0.0818500i | ||||
\(79\) | − | 5010.15i | − | 0.802780i | −0.915907 | − | 0.401390i | \(-0.868527\pi\) | ||
0.915907 | − | 0.401390i | \(-0.131473\pi\) | |||||||
\(80\) | 1340.21 | − | 873.970i | 0.209409 | − | 0.136558i | ||||
\(81\) | 1573.07 | 0.239761 | ||||||||
\(82\) | 3001.47 | + | 3001.47i | 0.446382 | + | 0.446382i | ||||
\(83\) | 3638.73 | − | 3638.73i | 0.528194 | − | 0.528194i | −0.391839 | − | 0.920034i | \(-0.628161\pi\) |
0.920034 | + | 0.391839i | \(0.128161\pi\) | |||||||
\(84\) | − | 1104.27i | − | 0.156500i | ||||||
\(85\) | 241.349 | + | 50.8213i | 0.0334047 | + | 0.00703409i | ||||
\(86\) | −2749.21 | −0.371716 | ||||||||
\(87\) | −6367.32 | − | 6367.32i | −0.841237 | − | 0.841237i | ||||
\(88\) | 2138.26 | − | 2138.26i | 0.276118 | − | 0.276118i | ||||
\(89\) | − | 12022.9i | − | 1.51786i | −0.651175 | − | 0.758928i | \(-0.725724\pi\) | ||
0.651175 | − | 0.758928i | \(-0.274276\pi\) | |||||||
\(90\) | −596.117 | + | 2830.95i | −0.0735947 | + | 0.349500i | ||||
\(91\) | 857.363 | 0.103534 | ||||||||
\(92\) | −623.974 | − | 623.974i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | −491.903 | + | 491.903i | −0.0568740 | + | 0.0568740i | ||||
\(94\) | 390.005i | 0.0441382i | ||||||||
\(95\) | 7946.84 | + | 12186.3i | 0.880537 | + | 1.35028i | ||||
\(96\) | 1146.10 | 0.124360 | ||||||||
\(97\) | 897.842 | + | 897.842i | 0.0954238 | + | 0.0954238i | 0.753207 | − | 0.657783i | \(-0.228506\pi\) |
−0.657783 | + | 0.753207i | \(0.728506\pi\) | |||||||
\(98\) | −3851.39 | + | 3851.39i | −0.401020 | + | 0.401020i | ||||
\(99\) | 5467.75i | 0.557877i | ||||||||
\(100\) | 4575.42 | + | 2016.31i | 0.457542 | + | 0.201631i | ||||
\(101\) | 6434.40 | 0.630762 | 0.315381 | − | 0.948965i | \(-0.397868\pi\) | ||||
0.315381 | + | 0.948965i | \(0.397868\pi\) | |||||||
\(102\) | 124.927 | + | 124.927i | 0.0120076 | + | 0.0120076i | ||||
\(103\) | −13926.1 | + | 13926.1i | −1.31267 | + | 1.31267i | −0.393221 | + | 0.919444i | \(0.628639\pi\) |
−0.919444 | + | 0.393221i | \(0.871361\pi\) | |||||||
\(104\) | 889.845i | 0.0822712i | ||||||||
\(105\) | 2890.53 | − | 1884.95i | 0.262180 | − | 0.170971i | ||||
\(106\) | −9828.37 | −0.874722 | ||||||||
\(107\) | 8513.25 | + | 8513.25i | 0.743581 | + | 0.743581i | 0.973265 | − | 0.229684i | \(-0.0737694\pi\) |
−0.229684 | + | 0.973265i | \(0.573769\pi\) | |||||||
\(108\) | −4366.42 | + | 4366.42i | −0.374350 | + | 0.374350i | ||||
\(109\) | − | 6247.33i | − | 0.525826i | −0.964820 | − | 0.262913i | \(-0.915317\pi\) | ||
0.964820 | − | 0.262913i | \(-0.0846832\pi\) | |||||||
\(110\) | 9247.08 | + | 1947.17i | 0.764221 | + | 0.160923i | ||||
\(111\) | 3113.88 | 0.252730 | ||||||||
\(112\) | 986.621 | + | 986.621i | 0.0786528 | + | 0.0786528i | ||||
\(113\) | 2797.66 | − | 2797.66i | 0.219098 | − | 0.219098i | −0.589020 | − | 0.808118i | \(-0.700486\pi\) |
0.808118 | + | 0.589020i | \(0.200486\pi\) | |||||||
\(114\) | 10421.3i | 0.801884i | ||||||||
\(115\) | 568.212 | − | 2698.43i | 0.0429650 | − | 0.204040i | ||||
\(116\) | 11377.9 | 0.845566 | ||||||||
\(117\) | −1137.71 | − | 1137.71i | −0.0831114 | − | 0.0831114i | ||||
\(118\) | −7657.41 | + | 7657.41i | −0.549943 | + | 0.549943i | ||||
\(119\) | 215.086i | 0.0151886i | ||||||||
\(120\) | 1956.37 | + | 3000.05i | 0.135859 | + | 0.208337i | ||||
\(121\) | 3218.99 | 0.219861 | ||||||||
\(122\) | 10132.5 | + | 10132.5i | 0.680765 | + | 0.680765i | ||||
\(123\) | −6718.74 | + | 6718.74i | −0.444097 | + | 0.444097i | ||||
\(124\) | − | 878.994i | − | 0.0571666i | ||||||
\(125\) | 2532.21 | + | 15418.4i | 0.162061 | + | 0.986781i | ||||
\(126\) | −2522.89 | −0.158912 | ||||||||
\(127\) | 8109.16 | + | 8109.16i | 0.502769 | + | 0.502769i | 0.912297 | − | 0.409529i | \(-0.134307\pi\) |
−0.409529 | + | 0.912297i | \(0.634307\pi\) | |||||||
\(128\) | −1024.00 | + | 1024.00i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 6154.06i | − | 0.369813i | ||||||
\(130\) | −2329.26 | + | 1518.94i | −0.137826 | + | 0.0898782i | ||||
\(131\) | 30412.4 | 1.77218 | 0.886090 | − | 0.463514i | \(-0.153412\pi\) | ||||
0.886090 | + | 0.463514i | \(0.153412\pi\) | |||||||
\(132\) | 4786.46 | + | 4786.46i | 0.274705 | + | 0.274705i | ||||
\(133\) | −8971.15 | + | 8971.15i | −0.507160 | + | 0.507160i | ||||
\(134\) | − | 6090.02i | − | 0.339164i | ||||||
\(135\) | −18882.9 | − | 3976.21i | −1.03610 | − | 0.218173i | ||||
\(136\) | −223.235 | −0.0120694 | ||||||||
\(137\) | −2657.43 | − | 2657.43i | −0.141586 | − | 0.141586i | 0.632761 | − | 0.774347i | \(-0.281922\pi\) |
−0.774347 | + | 0.632761i | \(0.781922\pi\) | |||||||
\(138\) | 1396.75 | − | 1396.75i | 0.0733436 | − | 0.0733436i | ||||
\(139\) | 1120.78i | 0.0580085i | 0.999579 | + | 0.0290043i | \(0.00923364\pi\) | ||||
−0.999579 | + | 0.0290043i | \(0.990766\pi\) | |||||||
\(140\) | −898.451 | + | 4266.72i | −0.0458393 | + | 0.217690i | ||||
\(141\) | −873.019 | −0.0439122 | ||||||||
\(142\) | 2794.94 | + | 2794.94i | 0.138611 | + | 0.138611i | ||||
\(143\) | −3716.25 | + | 3716.25i | −0.181733 | + | 0.181733i | ||||
\(144\) | − | 2618.47i | − | 0.126277i | ||||||
\(145\) | 19421.8 | + | 29783.0i | 0.923750 | + | 1.41655i | ||||
\(146\) | −5049.91 | −0.236907 | ||||||||
\(147\) | −8621.27 | − | 8621.27i | −0.398967 | − | 0.398967i | ||||
\(148\) | −2782.14 | + | 2782.14i | −0.127015 | + | 0.127015i | ||||
\(149\) | − | 16434.1i | − | 0.740243i | −0.928983 | − | 0.370122i | \(-0.879316\pi\) | ||
0.928983 | − | 0.370122i | \(-0.120684\pi\) | |||||||
\(150\) | −4513.48 | + | 10242.0i | −0.200599 | + | 0.455200i | ||||
\(151\) | 25320.6 | 1.11051 | 0.555253 | − | 0.831682i | \(-0.312621\pi\) | ||||
0.555253 | + | 0.831682i | \(0.312621\pi\) | |||||||
\(152\) | −9311.04 | − | 9311.04i | −0.403005 | − | 0.403005i | ||||
\(153\) | 285.417 | − | 285.417i | 0.0121926 | − | 0.0121926i | ||||
\(154\) | 8240.83i | 0.347480i | ||||||||
\(155\) | 2300.86 | − | 1500.42i | 0.0957694 | − | 0.0624524i | ||||
\(156\) | −1991.90 | −0.0818500 | ||||||||
\(157\) | 19257.5 | + | 19257.5i | 0.781271 | + | 0.781271i | 0.980045 | − | 0.198774i | \(-0.0636961\pi\) |
−0.198774 | + | 0.980045i | \(0.563696\pi\) | |||||||
\(158\) | −10020.3 | + | 10020.3i | −0.401390 | + | 0.401390i | ||||
\(159\) | − | 22000.6i | − | 0.870244i | ||||||
\(160\) | −4428.37 | − | 932.489i | −0.172983 | − | 0.0364254i | ||||
\(161\) | 2404.79 | 0.0927738 | ||||||||
\(162\) | −3146.15 | − | 3146.15i | −0.119881 | − | 0.119881i | ||||
\(163\) | 23703.8 | − | 23703.8i | 0.892162 | − | 0.892162i | −0.102564 | − | 0.994726i | \(-0.532705\pi\) |
0.994726 | + | 0.102564i | \(0.0327048\pi\) | |||||||
\(164\) | − | 12005.9i | − | 0.446382i | ||||||
\(165\) | −4358.71 | + | 20699.4i | −0.160099 | + | 0.760309i | ||||
\(166\) | −14554.9 | −0.528194 | ||||||||
\(167\) | 907.579 | + | 907.579i | 0.0325425 | + | 0.0325425i | 0.723191 | − | 0.690648i | \(-0.242675\pi\) |
−0.690648 | + | 0.723191i | \(0.742675\pi\) | |||||||
\(168\) | −2208.53 | + | 2208.53i | −0.0782501 | + | 0.0782501i | ||||
\(169\) | 27014.5i | 0.945852i | ||||||||
\(170\) | −381.056 | − | 584.341i | −0.0131853 | − | 0.0202194i | ||||
\(171\) | 23809.3 | 0.814242 | ||||||||
\(172\) | 5498.43 | + | 5498.43i | 0.185858 | + | 0.185858i | ||||
\(173\) | 21438.6 | − | 21438.6i | 0.716314 | − | 0.716314i | −0.251534 | − | 0.967848i | \(-0.580935\pi\) |
0.967848 | + | 0.251534i | \(0.0809351\pi\) | |||||||
\(174\) | 25469.3i | 0.841237i | ||||||||
\(175\) | −12702.2 | + | 4931.39i | −0.414767 | + | 0.161025i | ||||
\(176\) | −8553.04 | −0.276118 | ||||||||
\(177\) | −17141.0 | − | 17141.0i | −0.547128 | − | 0.547128i | ||||
\(178\) | −24045.9 | + | 24045.9i | −0.758928 | + | 0.758928i | ||||
\(179\) | − | 20851.2i | − | 0.650767i | −0.945582 | − | 0.325384i | \(-0.894507\pi\) | ||
0.945582 | − | 0.325384i | \(-0.105493\pi\) | |||||||
\(180\) | 6854.13 | − | 4469.66i | 0.211547 | − | 0.137952i | ||||
\(181\) | −17991.9 | −0.549185 | −0.274593 | − | 0.961561i | \(-0.588543\pi\) | ||||
−0.274593 | + | 0.961561i | \(0.588543\pi\) | |||||||
\(182\) | −1714.73 | − | 1714.73i | −0.0517669 | − | 0.0517669i | ||||
\(183\) | −22681.4 | + | 22681.4i | −0.677279 | + | 0.677279i | ||||
\(184\) | 2495.90i | 0.0737210i | ||||||||
\(185\) | −12031.6 | − | 2533.51i | −0.351544 | − | 0.0740251i | ||||
\(186\) | 1967.61 | 0.0568740 | ||||||||
\(187\) | −932.294 | − | 932.294i | −0.0266606 | − | 0.0266606i | ||||
\(188\) | 780.010 | − | 780.010i | 0.0220691 | − | 0.0220691i | ||||
\(189\) | − | 16828.1i | − | 0.471099i | ||||||
\(190\) | 8478.95 | − | 40266.3i | 0.234874 | − | 1.11541i | ||||
\(191\) | 35596.9 | 0.975764 | 0.487882 | − | 0.872910i | \(-0.337770\pi\) | ||||
0.487882 | + | 0.872910i | \(0.337770\pi\) | |||||||
\(192\) | −2292.20 | − | 2292.20i | −0.0621800 | − | 0.0621800i | ||||
\(193\) | −9427.48 | + | 9427.48i | −0.253094 | + | 0.253094i | −0.822238 | − | 0.569144i | \(-0.807275\pi\) |
0.569144 | + | 0.822238i | \(0.307275\pi\) | |||||||
\(194\) | − | 3591.37i | − | 0.0954238i | ||||||
\(195\) | −3400.12 | − | 5214.01i | −0.0894181 | − | 0.137121i | ||||
\(196\) | 15405.6 | 0.401020 | ||||||||
\(197\) | −28233.3 | − | 28233.3i | −0.727492 | − | 0.727492i | 0.242627 | − | 0.970120i | \(-0.421991\pi\) |
−0.970120 | + | 0.242627i | \(0.921991\pi\) | |||||||
\(198\) | 10935.5 | − | 10935.5i | 0.278938 | − | 0.278938i | ||||
\(199\) | 2118.93i | 0.0535069i | 0.999642 | + | 0.0267534i | \(0.00851690\pi\) | ||||
−0.999642 | + | 0.0267534i | \(0.991483\pi\) | |||||||
\(200\) | −5118.22 | − | 13183.5i | −0.127955 | − | 0.329587i | ||||
\(201\) | 13632.4 | 0.337427 | ||||||||
\(202\) | −12868.8 | − | 12868.8i | −0.315381 | − | 0.315381i | ||||
\(203\) | −21925.2 | + | 21925.2i | −0.532049 | + | 0.532049i | ||||
\(204\) | − | 499.707i | − | 0.0120076i | ||||||
\(205\) | 31426.7 | − | 20493.7i | 0.747810 | − | 0.487656i | ||||
\(206\) | 55704.3 | 1.31267 | ||||||||
\(207\) | −3191.13 | − | 3191.13i | −0.0744739 | − | 0.0744739i | ||||
\(208\) | 1779.69 | − | 1779.69i | 0.0411356 | − | 0.0411356i | ||||
\(209\) | − | 77771.2i | − | 1.78043i | ||||||
\(210\) | −9550.98 | − | 2011.16i | −0.216575 | − | 0.0456046i | ||||
\(211\) | −86409.8 | −1.94088 | −0.970439 | − | 0.241348i | \(-0.922410\pi\) | ||||
−0.970439 | + | 0.241348i | \(0.922410\pi\) | |||||||
\(212\) | 19656.7 | + | 19656.7i | 0.437361 | + | 0.437361i | ||||
\(213\) | −6256.43 | + | 6256.43i | −0.137901 | + | 0.137901i | ||||
\(214\) | − | 34053.0i | − | 0.743581i | ||||||
\(215\) | −5007.06 | + | 23778.4i | −0.108319 | + | 0.514406i | ||||
\(216\) | 17465.7 | 0.374350 | ||||||||
\(217\) | 1693.82 | + | 1693.82i | 0.0359705 | + | 0.0359705i | ||||
\(218\) | −12494.7 | + | 12494.7i | −0.262913 | + | 0.262913i | ||||
\(219\) | − | 11304.1i | − | 0.235694i | ||||||
\(220\) | −14599.8 | − | 22388.5i | −0.301649 | − | 0.462572i | ||||
\(221\) | 387.977 | 0.00794368 | ||||||||
\(222\) | −6227.76 | − | 6227.76i | −0.126365 | − | 0.126365i | ||||
\(223\) | −53920.4 | + | 53920.4i | −1.08428 | + | 1.08428i | −0.0881796 | + | 0.996105i | \(0.528105\pi\) |
−0.996105 | + | 0.0881796i | \(0.971895\pi\) | |||||||
\(224\) | − | 3946.48i | − | 0.0786528i | ||||||
\(225\) | 23399.6 | + | 10311.8i | 0.462215 | + | 0.203690i | ||||
\(226\) | −11190.7 | −0.219098 | ||||||||
\(227\) | −58185.9 | − | 58185.9i | −1.12919 | − | 1.12919i | −0.990309 | − | 0.138879i | \(-0.955650\pi\) |
−0.138879 | − | 0.990309i | \(-0.544350\pi\) | |||||||
\(228\) | 20842.6 | − | 20842.6i | 0.400942 | − | 0.400942i | ||||
\(229\) | 102779.i | 1.95989i | 0.199260 | + | 0.979947i | \(0.436146\pi\) | ||||
−0.199260 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(230\) | −6533.28 | + | 4260.43i | −0.123502 | + | 0.0805374i | ||||
\(231\) | −18446.9 | −0.345701 | ||||||||
\(232\) | −22755.9 | − | 22755.9i | −0.422783 | − | 0.422783i | ||||
\(233\) | −7978.96 | + | 7978.96i | −0.146972 | + | 0.146972i | −0.776764 | − | 0.629792i | \(-0.783140\pi\) |
0.629792 | + | 0.776764i | \(0.283140\pi\) | |||||||
\(234\) | 4550.85i | 0.0831114i | ||||||||
\(235\) | 3373.22 | + | 710.304i | 0.0610813 | + | 0.0128620i | ||||
\(236\) | 30629.6 | 0.549943 | ||||||||
\(237\) | −22430.2 | − | 22430.2i | −0.399335 | − | 0.399335i | ||||
\(238\) | 430.172 | − | 430.172i | 0.00759431 | − | 0.00759431i | ||||
\(239\) | − | 27188.7i | − | 0.475985i | −0.971267 | − | 0.237992i | \(-0.923511\pi\) | ||
0.971267 | − | 0.237992i | \(-0.0764894\pi\) | |||||||
\(240\) | 2087.36 | − | 9912.82i | 0.0362389 | − | 0.172098i | ||||
\(241\) | 93444.7 | 1.60887 | 0.804434 | − | 0.594041i | \(-0.202468\pi\) | ||||
0.804434 | + | 0.594041i | \(0.202468\pi\) | |||||||
\(242\) | −6437.98 | − | 6437.98i | −0.109931 | − | 0.109931i | ||||
\(243\) | −37167.4 | + | 37167.4i | −0.629434 | + | 0.629434i | ||||
\(244\) | − | 40530.0i | − | 0.680765i | ||||||
\(245\) | 26296.9 | + | 40325.7i | 0.438099 | + | 0.671816i | ||||
\(246\) | 26875.0 | 0.444097 | ||||||||
\(247\) | 16182.4 | + | 16182.4i | 0.265246 | + | 0.265246i | ||||
\(248\) | −1757.99 | + | 1757.99i | −0.0285833 | + | 0.0285833i | ||||
\(249\) | − | 32580.9i | − | 0.525490i | ||||||
\(250\) | 25772.5 | − | 35901.3i | 0.412360 | − | 0.574421i | ||||
\(251\) | −86697.4 | −1.37613 | −0.688064 | − | 0.725650i | \(-0.741539\pi\) | ||||
−0.688064 | + | 0.725650i | \(0.741539\pi\) | |||||||
\(252\) | 5045.78 | + | 5045.78i | 0.0794561 | + | 0.0794561i | ||||
\(253\) | −10423.6 | + | 10423.6i | −0.162846 | + | 0.162846i | ||||
\(254\) | − | 32436.6i | − | 0.502769i | ||||||
\(255\) | 1308.04 | − | 852.987i | 0.0201159 | − | 0.0131178i | ||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −43371.9 | − | 43371.9i | −0.656663 | − | 0.656663i | 0.297926 | − | 0.954589i | \(-0.403705\pi\) |
−0.954589 | + | 0.297926i | \(0.903705\pi\) | |||||||
\(258\) | −12308.1 | + | 12308.1i | −0.184907 | + | 0.184907i | ||||
\(259\) | − | 10722.3i | − | 0.159841i | ||||||
\(260\) | 7696.41 | + | 1620.65i | 0.113852 | + | 0.0239741i | ||||
\(261\) | 58189.1 | 0.854202 | ||||||||
\(262\) | −60824.7 | − | 60824.7i | −0.886090 | − | 0.886090i | ||||
\(263\) | 19131.9 | − | 19131.9i | 0.276597 | − | 0.276597i | −0.555152 | − | 0.831749i | \(-0.687340\pi\) |
0.831749 | + | 0.555152i | \(0.187340\pi\) | |||||||
\(264\) | − | 19145.8i | − | 0.274705i | ||||||
\(265\) | −17900.1 | + | 85007.2i | −0.254896 | + | 1.21050i | ||||
\(266\) | 35884.6 | 0.507160 | ||||||||
\(267\) | −53826.2 | − | 53826.2i | −0.755042 | − | 0.755042i | ||||
\(268\) | −12180.0 | + | 12180.0i | −0.169582 | + | 0.169582i | ||||
\(269\) | 93021.2i | 1.28552i | 0.766070 | + | 0.642758i | \(0.222210\pi\) | ||||
−0.766070 | + | 0.642758i | \(0.777790\pi\) | |||||||
\(270\) | 29813.5 | + | 45718.3i | 0.408964 | + | 0.627137i | ||||
\(271\) | −83220.8 | −1.13316 | −0.566582 | − | 0.824005i | \(-0.691735\pi\) | ||||
−0.566582 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(272\) | 446.470 | + | 446.470i | 0.00603468 | + | 0.00603468i | ||||
\(273\) | 3838.38 | − | 3838.38i | 0.0515018 | − | 0.0515018i | ||||
\(274\) | 10629.7i | 0.141586i | ||||||||
\(275\) | 33682.8 | − | 76433.1i | 0.445393 | − | 1.01069i | ||||
\(276\) | −5587.02 | −0.0733436 | ||||||||
\(277\) | −67889.2 | − | 67889.2i | −0.884792 | − | 0.884792i | 0.109225 | − | 0.994017i | \(-0.465163\pi\) |
−0.994017 | + | 0.109225i | \(0.965163\pi\) | |||||||
\(278\) | 2241.57 | − | 2241.57i | 0.0290043 | − | 0.0290043i | ||||
\(279\) | − | 4495.35i | − | 0.0577505i | ||||||
\(280\) | 10330.3 | − | 6736.54i | 0.131765 | − | 0.0859253i | ||||
\(281\) | 37774.9 | 0.478400 | 0.239200 | − | 0.970970i | \(-0.423115\pi\) | ||||
0.239200 | + | 0.970970i | \(0.423115\pi\) | |||||||
\(282\) | 1746.04 | + | 1746.04i | 0.0219561 | + | 0.0219561i | ||||
\(283\) | 19303.8 | − | 19303.8i | 0.241030 | − | 0.241030i | −0.576246 | − | 0.817276i | \(-0.695483\pi\) |
0.817276 | + | 0.576246i | \(0.195483\pi\) | |||||||
\(284\) | − | 11179.8i | − | 0.138611i | ||||||
\(285\) | 90135.4 | + | 18980.0i | 1.10970 | + | 0.233671i | ||||
\(286\) | 14865.0 | 0.181733 | ||||||||
\(287\) | 23135.3 | + | 23135.3i | 0.280874 | + | 0.280874i | ||||
\(288\) | −5236.94 | + | 5236.94i | −0.0631383 | + | 0.0631383i | ||||
\(289\) | − | 83423.7i | − | 0.998835i | ||||||
\(290\) | 20722.3 | − | 98409.6i | 0.246400 | − | 1.17015i | ||||
\(291\) | 8039.21 | 0.0949353 | ||||||||
\(292\) | 10099.8 | + | 10099.8i | 0.118453 | + | 0.118453i | ||||
\(293\) | −28464.3 | + | 28464.3i | −0.331562 | + | 0.331562i | −0.853180 | − | 0.521617i | \(-0.825329\pi\) |
0.521617 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(294\) | 34485.1i | 0.398967i | ||||||||
\(295\) | 52283.9 | + | 80176.3i | 0.600792 | + | 0.921302i | ||||
\(296\) | 11128.5 | 0.127015 | ||||||||
\(297\) | 72941.8 | + | 72941.8i | 0.826920 | + | 0.826920i | ||||
\(298\) | −32868.3 | + | 32868.3i | −0.370122 | + | 0.370122i | ||||
\(299\) | − | 4337.82i | − | 0.0485209i | ||||||
\(300\) | 29510.9 | − | 11457.0i | 0.327899 | − | 0.127300i | ||||
\(301\) | −21190.9 | −0.233892 | ||||||||
\(302\) | −50641.3 | − | 50641.3i | −0.555253 | − | 0.555253i | ||||
\(303\) | 28806.6 | − | 28806.6i | 0.313766 | − | 0.313766i | ||||
\(304\) | 37244.1i | 0.403005i | ||||||||
\(305\) | 106092. | − | 69183.6i | 1.14046 | − | 0.743710i | ||||
\(306\) | −1141.67 | −0.0121926 | ||||||||
\(307\) | −10051.9 | − | 10051.9i | −0.106652 | − | 0.106652i | 0.651767 | − | 0.758419i | \(-0.274028\pi\) |
−0.758419 | + | 0.651767i | \(0.774028\pi\) | |||||||
\(308\) | 16481.7 | − | 16481.7i | 0.173740 | − | 0.173740i | ||||
\(309\) | 124693.i | 1.30594i | ||||||||
\(310\) | −7602.56 | − | 1600.88i | −0.0791109 | − | 0.0166585i | ||||
\(311\) | −85798.1 | −0.887068 | −0.443534 | − | 0.896258i | \(-0.646275\pi\) | ||||
−0.443534 | + | 0.896258i | \(0.646275\pi\) | |||||||
\(312\) | 3983.80 | + | 3983.80i | 0.0409250 | + | 0.0409250i | ||||
\(313\) | −98508.8 | + | 98508.8i | −1.00551 | + | 1.00551i | −0.00552498 | + | 0.999985i | \(0.501759\pi\) |
−0.999985 | + | 0.00552498i | \(0.998241\pi\) | |||||||
\(314\) | − | 77030.2i | − | 0.781271i | ||||||
\(315\) | −4594.86 | + | 21820.9i | −0.0463075 | + | 0.219913i | ||||
\(316\) | 40081.2 | 0.401390 | ||||||||
\(317\) | 96104.3 | + | 96104.3i | 0.956366 | + | 0.956366i | 0.999087 | − | 0.0427210i | \(-0.0136027\pi\) |
−0.0427210 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(318\) | −44001.3 | + | 44001.3i | −0.435122 | + | 0.435122i | ||||
\(319\) | − | 190070.i | − | 1.86781i | ||||||
\(320\) | 6991.76 | + | 10721.7i | 0.0682789 | + | 0.104704i | ||||
\(321\) | 76227.0 | 0.739774 | ||||||||
\(322\) | −4809.58 | − | 4809.58i | −0.0463869 | − | 0.0463869i | ||||
\(323\) | −4059.66 | + | 4059.66i | −0.0389121 | + | 0.0389121i | ||||
\(324\) | 12584.6i | 0.119881i | ||||||||
\(325\) | 8895.35 | + | 22912.6i | 0.0842164 | + | 0.216924i | ||||
\(326\) | −94815.4 | −0.892162 | ||||||||
\(327\) | −27969.1 | − | 27969.1i | −0.261567 | − | 0.261567i | ||||
\(328\) | −24011.8 | + | 24011.8i | −0.223191 | + | 0.223191i | ||||
\(329\) | 3006.15i | 0.0277727i | ||||||||
\(330\) | 50116.2 | − | 32681.4i | 0.460204 | − | 0.300105i | ||||
\(331\) | −11449.0 | −0.104499 | −0.0522494 | − | 0.998634i | \(-0.516639\pi\) | ||||
−0.0522494 | + | 0.998634i | \(0.516639\pi\) | |||||||
\(332\) | 29109.8 | + | 29109.8i | 0.264097 | + | 0.264097i | ||||
\(333\) | −14228.4 | + | 14228.4i | −0.128312 | + | 0.128312i | ||||
\(334\) | − | 3630.32i | − | 0.0325425i | ||||||
\(335\) | −52673.6 | − | 11091.6i | −0.469357 | − | 0.0988332i | ||||
\(336\) | 8834.13 | 0.0782501 | ||||||||
\(337\) | 142320. | + | 142320.i | 1.25316 | + | 1.25316i | 0.954295 | + | 0.298865i | \(0.0966082\pi\) |
0.298865 | + | 0.954295i | \(0.403392\pi\) | |||||||
\(338\) | 54028.9 | − | 54028.9i | 0.472926 | − | 0.472926i | ||||
\(339\) | − | 25050.1i | − | 0.217976i | ||||||
\(340\) | −406.571 | + | 1930.79i | −0.00351705 | + | 0.0167024i | ||||
\(341\) | −14683.7 | −0.126278 | ||||||||
\(342\) | −47618.5 | − | 47618.5i | −0.407121 | − | 0.407121i | ||||
\(343\) | −66700.1 | + | 66700.1i | −0.566942 | + | 0.566942i | ||||
\(344\) | − | 21993.7i | − | 0.185858i | ||||||
\(345\) | −9536.89 | − | 14624.6i | −0.0801251 | − | 0.122870i | ||||
\(346\) | −85754.3 | −0.716314 | ||||||||
\(347\) | −6898.82 | − | 6898.82i | −0.0572949 | − | 0.0572949i | 0.677879 | − | 0.735174i | \(-0.262899\pi\) |
−0.735174 | + | 0.677879i | \(0.762899\pi\) | |||||||
\(348\) | 50938.6 | − | 50938.6i | 0.420619 | − | 0.420619i | ||||
\(349\) | − | 120582.i | − | 0.989989i | −0.868896 | − | 0.494994i | \(-0.835170\pi\) | ||
0.868896 | − | 0.494994i | \(-0.164830\pi\) | |||||||
\(350\) | 35267.2 | + | 15541.7i | 0.287896 | + | 0.126871i | ||||
\(351\) | −30355.0 | −0.246386 | ||||||||
\(352\) | 17106.1 | + | 17106.1i | 0.138059 | + | 0.138059i | ||||
\(353\) | 99139.7 | − | 99139.7i | 0.795606 | − | 0.795606i | −0.186793 | − | 0.982399i | \(-0.559809\pi\) |
0.982399 | + | 0.186793i | \(0.0598095\pi\) | |||||||
\(354\) | 68563.8i | 0.547128i | ||||||||
\(355\) | 29264.3 | − | 19083.6i | 0.232210 | − | 0.151427i | ||||
\(356\) | 96183.5 | 0.758928 | ||||||||
\(357\) | 962.932 | + | 962.932i | 0.00755543 | + | 0.00755543i | ||||
\(358\) | −41702.5 | + | 41702.5i | −0.325384 | + | 0.325384i | ||||
\(359\) | 66147.1i | 0.513242i | 0.966512 | + | 0.256621i | \(0.0826092\pi\) | ||||
−0.966512 | + | 0.256621i | \(0.917391\pi\) | |||||||
\(360\) | −22647.6 | − | 4768.94i | −0.174750 | − | 0.0367974i | ||||
\(361\) | −208333. | −1.59861 | ||||||||
\(362\) | 35983.7 | + | 35983.7i | 0.274593 | + | 0.274593i | ||||
\(363\) | 14411.3 | − | 14411.3i | 0.109368 | − | 0.109368i | ||||
\(364\) | 6858.90i | 0.0517669i | ||||||||
\(365\) | −9197.24 | + | 43677.5i | −0.0690354 | + | 0.327847i | ||||
\(366\) | 90725.6 | 0.677279 | ||||||||
\(367\) | −109978. | − | 109978.i | −0.816531 | − | 0.816531i | 0.169073 | − | 0.985604i | \(-0.445923\pi\) |
−0.985604 | + | 0.169073i | \(0.945923\pi\) | |||||||
\(368\) | 4991.79 | − | 4991.79i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 61400.6i | − | 0.450941i | ||||||
\(370\) | 18996.1 | + | 29130.2i | 0.138759 | + | 0.212784i | ||||
\(371\) | −75756.9 | −0.550395 | ||||||||
\(372\) | −3935.22 | − | 3935.22i | −0.0284370 | − | 0.0284370i | ||||
\(373\) | −62523.6 | + | 62523.6i | −0.449393 | + | 0.449393i | −0.895153 | − | 0.445760i | \(-0.852934\pi\) |
0.445760 | + | 0.895153i | \(0.352934\pi\) | |||||||
\(374\) | 3729.17i | 0.0266606i | ||||||||
\(375\) | 80364.4 | + | 57691.2i | 0.571480 | + | 0.410249i | ||||
\(376\) | −3120.04 | −0.0220691 | ||||||||
\(377\) | 39549.2 | + | 39549.2i | 0.278263 | + | 0.278263i | ||||
\(378\) | −33656.3 | + | 33656.3i | −0.235550 | + | 0.235550i | ||||
\(379\) | 110606.i | 0.770014i | 0.922914 | + | 0.385007i | \(0.125801\pi\) | ||||
−0.922914 | + | 0.385007i | \(0.874199\pi\) | |||||||
\(380\) | −97490.5 | + | 63574.8i | −0.675142 | + | 0.440268i | ||||
\(381\) | 72608.8 | 0.500195 | ||||||||
\(382\) | −71193.7 | − | 71193.7i | −0.487882 | − | 0.487882i | ||||
\(383\) | −1184.54 | + | 1184.54i | −0.00807515 | + | 0.00807515i | −0.711133 | − | 0.703058i | \(-0.751818\pi\) |
0.703058 | + | 0.711133i | \(0.251818\pi\) | |||||||
\(384\) | 9168.82i | 0.0621800i | ||||||||
\(385\) | 71276.3 | + | 15008.8i | 0.480865 | + | 0.101257i | ||||
\(386\) | 37709.9 | 0.253094 | ||||||||
\(387\) | 28120.1 | + | 28120.1i | 0.187756 | + | 0.187756i | ||||
\(388\) | −7182.74 | + | 7182.74i | −0.0477119 | + | 0.0477119i | ||||
\(389\) | 45967.0i | 0.303771i | 0.988398 | + | 0.151886i | \(0.0485345\pi\) | ||||
−0.988398 | + | 0.151886i | \(0.951465\pi\) | |||||||
\(390\) | −3627.79 | + | 17228.3i | −0.0238513 | + | 0.113269i | ||||
\(391\) | 1088.23 | 0.00711812 | ||||||||
\(392\) | −30811.2 | − | 30811.2i | −0.200510 | − | 0.200510i | ||||
\(393\) | 136155. | − | 136155.i | 0.881553 | − | 0.881553i | ||||
\(394\) | 112933.i | 0.727492i | ||||||||
\(395\) | 68417.5 | + | 104917.i | 0.438504 | + | 0.672436i | ||||
\(396\) | −43742.0 | −0.278938 | ||||||||
\(397\) | −159089. | − | 159089.i | −1.00939 | − | 1.00939i | −0.999956 | − | 0.00943206i | \(-0.996998\pi\) |
−0.00943206 | − | 0.999956i | \(-0.503002\pi\) | |||||||
\(398\) | 4237.85 | − | 4237.85i | 0.0267534 | − | 0.0267534i | ||||
\(399\) | 80327.0i | 0.504564i | ||||||||
\(400\) | −16130.5 | + | 36603.4i | −0.100816 | + | 0.228771i | ||||
\(401\) | 126144. | 0.784475 | 0.392238 | − | 0.919864i | \(-0.371701\pi\) | ||||
0.392238 | + | 0.919864i | \(0.371701\pi\) | |||||||
\(402\) | −27264.8 | − | 27264.8i | −0.168714 | − | 0.168714i | ||||
\(403\) | 3055.34 | − | 3055.34i | 0.0188127 | − | 0.0188127i | ||||
\(404\) | 51475.2i | 0.315381i | ||||||||
\(405\) | −32941.5 | + | 21481.5i | −0.200832 | + | 0.130965i | ||||
\(406\) | 87700.9 | 0.532049 | ||||||||
\(407\) | 46476.0 | + | 46476.0i | 0.280569 | + | 0.280569i | ||||
\(408\) | −999.414 | + | 999.414i | −0.00600379 | + | 0.00600379i | ||||
\(409\) | 147744.i | 0.883208i | 0.897210 | + | 0.441604i | \(0.145590\pi\) | ||||
−0.897210 | + | 0.441604i | \(0.854410\pi\) | |||||||
\(410\) | −103841. | − | 21866.0i | −0.617733 | − | 0.130077i | ||||
\(411\) | −23794.4 | −0.140861 | ||||||||
\(412\) | −111409. | − | 111409.i | −0.656333 | − | 0.656333i | ||||
\(413\) | −59023.1 | + | 59023.1i | −0.346036 | + | 0.346036i | ||||
\(414\) | 12764.5i | 0.0744739i | ||||||||
\(415\) | −26508.4 | + | 125888.i | −0.153917 | + | 0.730950i | ||||
\(416\) | −7118.76 | −0.0411356 | ||||||||
\(417\) | 5017.70 | + | 5017.70i | 0.0288558 | + | 0.0288558i | ||||
\(418\) | −155542. | + | 155542.i | −0.890217 | + | 0.890217i | ||||
\(419\) | 203624.i | 1.15985i | 0.814672 | + | 0.579923i | \(0.196917\pi\) | ||||
−0.814672 | + | 0.579923i | \(0.803083\pi\) | |||||||
\(420\) | 15079.6 | + | 23124.3i | 0.0854854 | + | 0.131090i | ||||
\(421\) | −113865. | −0.642431 | −0.321215 | − | 0.947006i | \(-0.604091\pi\) | ||||
−0.321215 | + | 0.947006i | \(0.604091\pi\) | |||||||
\(422\) | 172820. | + | 172820.i | 0.970439 | + | 0.970439i | ||||
\(423\) | 3989.13 | − | 3989.13i | 0.0222945 | − | 0.0222945i | ||||
\(424\) | − | 78627.0i | − | 0.437361i | ||||||
\(425\) | −5748.07 | + | 2231.57i | −0.0318232 | + | 0.0123547i | ||||
\(426\) | 25025.7 | 0.137901 | ||||||||
\(427\) | 78101.1 | + | 78101.1i | 0.428352 | + | 0.428352i | ||||
\(428\) | −68106.0 | + | 68106.0i | −0.371790 | + | 0.371790i | ||||
\(429\) | 33275.0i | 0.180802i | ||||||||
\(430\) | 57570.9 | − | 37542.7i | 0.311362 | − | 0.203043i | ||||
\(431\) | −310369. | −1.67080 | −0.835400 | − | 0.549643i | \(-0.814764\pi\) | ||||
−0.835400 | + | 0.549643i | \(0.814764\pi\) | |||||||
\(432\) | −34931.4 | − | 34931.4i | −0.187175 | − | 0.187175i | ||||
\(433\) | −136164. | + | 136164.i | −0.726248 | + | 0.726248i | −0.969870 | − | 0.243622i | \(-0.921664\pi\) |
0.243622 | + | 0.969870i | \(0.421664\pi\) | |||||||
\(434\) | − | 6775.26i | − | 0.0359705i | ||||||
\(435\) | 220288. | + | 46386.4i | 1.16416 | + | 0.245139i | ||||
\(436\) | 49978.7 | 0.262913 | ||||||||
\(437\) | 45389.4 | + | 45389.4i | 0.237680 | + | 0.237680i | ||||
\(438\) | −22608.2 | + | 22608.2i | −0.117847 | + | 0.117847i | ||||
\(439\) | − | 297445.i | − | 1.54339i | −0.635990 | − | 0.771697i | \(-0.719408\pi\) | ||
0.635990 | − | 0.771697i | \(-0.280592\pi\) | |||||||
\(440\) | −15577.4 | + | 73976.6i | −0.0804617 | + | 0.382111i | ||||
\(441\) | 78787.2 | 0.405115 | ||||||||
\(442\) | −775.955 | − | 775.955i | −0.00397184 | − | 0.00397184i | ||||
\(443\) | 196943. | − | 196943.i | 1.00354 | − | 1.00354i | 0.00354489 | − | 0.999994i | \(-0.498872\pi\) |
0.999994 | − | 0.00354489i | \(-0.00112838\pi\) | |||||||
\(444\) | 24911.0i | 0.126365i | ||||||||
\(445\) | 164183. | + | 251771.i | 0.829100 | + | 1.27141i | ||||
\(446\) | 215681. | 1.08428 | ||||||||
\(447\) | −73575.0 | − | 73575.0i | −0.368227 | − | 0.368227i | ||||
\(448\) | −7892.97 | + | 7892.97i | −0.0393264 | + | 0.0393264i | ||||
\(449\) | − | 277579.i | − | 1.37687i | −0.725298 | − | 0.688435i | \(-0.758298\pi\) | ||
0.725298 | − | 0.688435i | \(-0.241702\pi\) | |||||||
\(450\) | −26175.6 | − | 67422.9i | −0.129262 | − | 0.332953i | ||||
\(451\) | −200560. | −0.986034 | ||||||||
\(452\) | 22381.3 | + | 22381.3i | 0.109549 | + | 0.109549i | ||||
\(453\) | 113360. | − | 113360.i | 0.552410 | − | 0.552410i | ||||
\(454\) | 232744.i | 1.12919i | ||||||||
\(455\) | −17953.9 | + | 11708.0i | −0.0867234 | + | 0.0565534i | ||||
\(456\) | −83370.3 | −0.400942 | ||||||||
\(457\) | 204991. | + | 204991.i | 0.981527 | + | 0.981527i | 0.999832 | − | 0.0183054i | \(-0.00582713\pi\) |
−0.0183054 | + | 0.999832i | \(0.505827\pi\) | |||||||
\(458\) | 205558. | − | 205558.i | 0.979947 | − | 0.979947i | ||||
\(459\) | − | 7615.14i | − | 0.0361453i | ||||||
\(460\) | 21587.4 | + | 4545.70i | 0.102020 | + | 0.0214825i | ||||
\(461\) | −3099.86 | −0.0145861 | −0.00729306 | − | 0.999973i | \(-0.502321\pi\) | ||||
−0.00729306 | + | 0.999973i | \(0.502321\pi\) | |||||||
\(462\) | 36893.9 | + | 36893.9i | 0.172850 | + | 0.172850i | ||||
\(463\) | 62253.8 | − | 62253.8i | 0.290405 | − | 0.290405i | −0.546835 | − | 0.837240i | \(-0.684168\pi\) |
0.837240 | + | 0.546835i | \(0.184168\pi\) | |||||||
\(464\) | 91023.5i | 0.422783i | ||||||||
\(465\) | 3583.55 | − | 17018.2i | 0.0165732 | − | 0.0787059i | ||||
\(466\) | 31915.8 | 0.146972 | ||||||||
\(467\) | 186901. | + | 186901.i | 0.856993 | + | 0.856993i | 0.990983 | − | 0.133990i | \(-0.0427789\pi\) |
−0.133990 | + | 0.990983i | \(0.542779\pi\) | |||||||
\(468\) | 9101.69 | − | 9101.69i | 0.0415557 | − | 0.0415557i | ||||
\(469\) | − | 46941.7i | − | 0.213409i | ||||||
\(470\) | −5325.82 | − | 8167.04i | −0.0241097 | − | 0.0369717i | ||||
\(471\) | 172431. | 0.777271 | ||||||||
\(472\) | −61259.2 | − | 61259.2i | −0.274971 | − | 0.274971i | ||||
\(473\) | 91852.1 | − | 91852.1i | 0.410551 | − | 0.410551i | ||||
\(474\) | 89721.0i | 0.399335i | ||||||||
\(475\) | −332827. | − | 146672.i | −1.47514 | − | 0.650068i | ||||
\(476\) | −1720.69 | −0.00759431 | ||||||||
\(477\) | 100529. | + | 100529.i | 0.441828 | + | 0.441828i | ||||
\(478\) | −54377.5 | + | 54377.5i | −0.237992 | + | 0.237992i | ||||
\(479\) | − | 83978.2i | − | 0.366012i | −0.983112 | − | 0.183006i | \(-0.941417\pi\) | ||
0.983112 | − | 0.183006i | \(-0.0585828\pi\) | |||||||
\(480\) | −24000.4 | + | 15650.9i | −0.104168 | + | 0.0679294i | ||||
\(481\) | −19341.2 | −0.0835974 | ||||||||
\(482\) | −186889. | − | 186889.i | −0.804434 | − | 0.804434i | ||||
\(483\) | 10766.2 | − | 10766.2i | 0.0461494 | − | 0.0461494i | ||||
\(484\) | 25751.9i | 0.109931i | ||||||||
\(485\) | −31062.3 | − | 6540.85i | −0.132054 | − | 0.0278068i | ||||
\(486\) | 148670. | 0.629434 | ||||||||
\(487\) | −239611. | − | 239611.i | −1.01030 | − | 1.01030i | −0.999946 | − | 0.0103487i | \(-0.996706\pi\) |
−0.0103487 | − | 0.999946i | \(-0.503294\pi\) | |||||||
\(488\) | −81060.0 | + | 81060.0i | −0.340382 | + | 0.340382i | ||||
\(489\) | − | 212242.i | − | 0.887594i | ||||||
\(490\) | 28057.7 | − | 133245.i | 0.116858 | − | 0.554958i | ||||
\(491\) | 58812.0 | 0.243951 | 0.121976 | − | 0.992533i | \(-0.461077\pi\) | ||||
0.121976 | + | 0.992533i | \(0.461077\pi\) | |||||||
\(492\) | −53749.9 | − | 53749.9i | −0.222048 | − | 0.222048i | ||||
\(493\) | −9921.69 | + | 9921.69i | −0.0408218 | + | 0.0408218i | ||||
\(494\) | − | 64729.5i | − | 0.265246i | ||||||
\(495\) | −74666.4 | − | 114499.i | −0.304730 | − | 0.467297i | ||||
\(496\) | 7031.95 | 0.0285833 | ||||||||
\(497\) | 21543.4 | + | 21543.4i | 0.0872169 | + | 0.0872169i | ||||
\(498\) | −65161.8 | + | 65161.8i | −0.262745 | + | 0.262745i | ||||
\(499\) | 173676.i | 0.697489i | 0.937218 | + | 0.348745i | \(0.113392\pi\) | ||||
−0.937218 | + | 0.348745i | \(0.886608\pi\) | |||||||
\(500\) | −123348. | + | 20257.7i | −0.493390 | + | 0.0810307i | ||||
\(501\) | 8126.39 | 0.0323759 | ||||||||
\(502\) | 173395. | + | 173395.i | 0.688064 | + | 0.688064i | ||||
\(503\) | −11620.5 | + | 11620.5i | −0.0459291 | + | 0.0459291i | −0.729698 | − | 0.683769i | \(-0.760339\pi\) |
0.683769 | + | 0.729698i | \(0.260339\pi\) | |||||||
\(504\) | − | 20183.1i | − | 0.0794561i | ||||||
\(505\) | −134742. | + | 87866.8i | −0.528348 | + | 0.344542i | ||||
\(506\) | 41694.4 | 0.162846 | ||||||||
\(507\) | 120943. | + | 120943.i | 0.470505 | + | 0.470505i | ||||
\(508\) | −64873.3 | + | 64873.3i | −0.251384 | + | 0.251384i | ||||
\(509\) | − | 326727.i | − | 1.26110i | −0.776149 | − | 0.630550i | \(-0.782829\pi\) | ||
0.776149 | − | 0.630550i | \(-0.217171\pi\) | |||||||
\(510\) | −4322.05 | − | 910.100i | −0.0166169 | − | 0.00349904i | ||||
\(511\) | −38924.6 | −0.149067 | ||||||||
\(512\) | −8192.00 | − | 8192.00i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 317624. | − | 317624.i | 1.20692 | − | 1.20692i | ||||
\(514\) | 173488.i | 0.656663i | ||||||||
\(515\) | 101452. | − | 481795.i | 0.382514 | − | 1.81655i | ||||
\(516\) | 49232.5 | 0.184907 | ||||||||
\(517\) | −13030.2 | − | 13030.2i | −0.0487494 | − | 0.0487494i | ||||
\(518\) | −21444.6 | + | 21444.6i | −0.0799207 | + | 0.0799207i | ||||
\(519\) | − | 191959.i | − | 0.712647i | ||||||
\(520\) | −12151.5 | − | 18634.1i | −0.0449391 | − | 0.0689131i | ||||
\(521\) | 397121. | 1.46301 | 0.731505 | − | 0.681836i | \(-0.238818\pi\) | ||||
0.731505 | + | 0.681836i | \(0.238818\pi\) | |||||||
\(522\) | −116378. | − | 116378.i | −0.427101 | − | 0.427101i | ||||
\(523\) | 299724. | − | 299724.i | 1.09577 | − | 1.09577i | 0.100866 | − | 0.994900i | \(-0.467839\pi\) |
0.994900 | − | 0.100866i | \(-0.0321613\pi\) | |||||||
\(524\) | 243299.i | 0.886090i | ||||||||
\(525\) | −34789.8 | + | 78945.0i | −0.126221 | + | 0.286422i | ||||
\(526\) | −76527.7 | −0.276597 | ||||||||
\(527\) | 766.493 | + | 766.493i | 0.00275986 | + | 0.00275986i | ||||
\(528\) | −38291.6 | + | 38291.6i | −0.137352 | + | 0.137352i | ||||
\(529\) | − | 12167.0i | − | 0.0434783i | ||||||
\(530\) | 205815. | − | 134214.i | 0.732697 | − | 0.477800i | ||||
\(531\) | 156646. | 0.555559 | ||||||||
\(532\) | −71769.2 | − | 71769.2i | −0.253580 | − | 0.253580i | ||||
\(533\) | 41732.0 | − | 41732.0i | 0.146898 | − | 0.146898i | ||||
\(534\) | 215305.i | 0.755042i | ||||||||
\(535\) | −294530. | − | 62019.7i | −1.02902 | − | 0.216682i | ||||
\(536\) | 48720.2 | 0.169582 | ||||||||
\(537\) | −93350.2 | − | 93350.2i | −0.323718 | − | 0.323718i | ||||
\(538\) | 186042. | − | 186042.i | 0.642758 | − | 0.642758i | ||||
\(539\) | − | 257353.i | − | 0.885831i | ||||||
\(540\) | 31809.7 | − | 151064.i | 0.109087 | − | 0.518050i | ||||
\(541\) | −329750. | −1.12665 | −0.563326 | − | 0.826235i | \(-0.690478\pi\) | ||||
−0.563326 | + | 0.826235i | \(0.690478\pi\) | |||||||
\(542\) | 166442. | + | 166442.i | 0.566582 | + | 0.566582i | ||||
\(543\) | −80548.9 | + | 80548.9i | −0.273187 | + | 0.273187i | ||||
\(544\) | − | 1785.88i | − | 0.00603468i | ||||||
\(545\) | 85312.3 | + | 130825.i | 0.287222 | + | 0.440450i | ||||
\(546\) | −15353.5 | −0.0515018 | ||||||||
\(547\) | −306007. | − | 306007.i | −1.02272 | − | 1.02272i | −0.999736 | − | 0.0229849i | \(-0.992683\pi\) |
−0.0229849 | − | 0.999736i | \(-0.507317\pi\) | |||||||
\(548\) | 21259.4 | − | 21259.4i | 0.0707931 | − | 0.0707931i | ||||
\(549\) | − | 207279.i | − | 0.687717i | ||||||
\(550\) | −220232. | + | 85500.7i | −0.728039 | + | 0.282647i | ||||
\(551\) | −827659. | −2.72614 | ||||||||
\(552\) | 11174.0 | + | 11174.0i | 0.0366718 | + | 0.0366718i | ||||
\(553\) | −77236.2 | + | 77236.2i | −0.252564 | + | 0.252564i | ||||
\(554\) | 271557.i | 0.884792i | ||||||||
\(555\) | −65207.3 | + | 42522.5i | −0.211695 | + | 0.138049i | ||||
\(556\) | −8966.26 | −0.0290043 | ||||||||
\(557\) | 272348. | + | 272348.i | 0.877837 | + | 0.877837i | 0.993311 | − | 0.115474i | \(-0.0368387\pi\) |
−0.115474 | + | 0.993311i | \(0.536839\pi\) | |||||||
\(558\) | −8990.71 | + | 8990.71i | −0.0288752 | + | 0.0288752i | ||||
\(559\) | 38224.6i | 0.122326i | ||||||||
\(560\) | −34133.8 | − | 7187.60i | −0.108845 | − | 0.0229197i | ||||
\(561\) | −8347.69 | −0.0265241 | ||||||||
\(562\) | −75549.8 | − | 75549.8i | −0.239200 | − | 0.239200i | ||||
\(563\) | −122342. | + | 122342.i | −0.385974 | + | 0.385974i | −0.873249 | − | 0.487275i | \(-0.837991\pi\) |
0.487275 | + | 0.873249i | \(0.337991\pi\) | |||||||
\(564\) | − | 6984.15i | − | 0.0219561i | ||||||
\(565\) | −20381.2 | + | 96789.8i | −0.0638458 | + | 0.303202i | ||||
\(566\) | −77215.4 | −0.241030 | ||||||||
\(567\) | −24250.4 | − | 24250.4i | −0.0754315 | − | 0.0754315i | ||||
\(568\) | −22359.6 | + | 22359.6i | −0.0693053 | + | 0.0693053i | ||||
\(569\) | − | 190163.i | − | 0.587355i | −0.955905 | − | 0.293678i | \(-0.905121\pi\) | ||
0.955905 | − | 0.293678i | \(-0.0948792\pi\) | |||||||
\(570\) | −142311. | − | 218231.i | −0.438014 | − | 0.671686i | ||||
\(571\) | −167852. | −0.514818 | −0.257409 | − | 0.966303i | \(-0.582869\pi\) | ||||
−0.257409 | + | 0.966303i | \(0.582869\pi\) | |||||||
\(572\) | −29730.0 | − | 29730.0i | −0.0908663 | − | 0.0908663i | ||||
\(573\) | 159366. | − | 159366.i | 0.485384 | − | 0.485384i | ||||
\(574\) | − | 92541.1i | − | 0.280874i | ||||||
\(575\) | 24950.3 | + | 64266.8i | 0.0754640 | + | 0.194380i | ||||
\(576\) | 20947.8 | 0.0631383 | ||||||||
\(577\) | 170670. | + | 170670.i | 0.512633 | + | 0.512633i | 0.915332 | − | 0.402700i | \(-0.131928\pi\) |
−0.402700 | + | 0.915332i | \(0.631928\pi\) | |||||||
\(578\) | −166847. | + | 166847.i | −0.499417 | + | 0.499417i | ||||
\(579\) | 84413.0i | 0.251798i | ||||||||
\(580\) | −238264. | + | 155375.i | −0.708275 | + | 0.461875i | ||||
\(581\) | −112189. | −0.332352 | ||||||||
\(582\) | −16078.4 | − | 16078.4i | −0.0474676 | − | 0.0474676i | ||||
\(583\) | 328369. | − | 328369.i | 0.966107 | − | 0.966107i | ||||
\(584\) | − | 40399.3i | − | 0.118453i | ||||||
\(585\) | 39361.0 | + | 8288.31i | 0.115015 | + | 0.0242189i | ||||
\(586\) | 113857. | 0.331562 | ||||||||
\(587\) | −125647. | − | 125647.i | −0.364651 | − | 0.364651i | 0.500871 | − | 0.865522i | \(-0.333013\pi\) |
−0.865522 | + | 0.500871i | \(0.833013\pi\) | |||||||
\(588\) | 68970.2 | − | 68970.2i | 0.199483 | − | 0.199483i | ||||
\(589\) | 63940.2i | 0.184308i | ||||||||
\(590\) | 55784.8 | − | 264921.i | 0.160255 | − | 0.761047i | ||||
\(591\) | −252798. | −0.723768 | ||||||||
\(592\) | −22257.1 | − | 22257.1i | −0.0635075 | − | 0.0635075i | ||||
\(593\) | −8108.29 | + | 8108.29i | −0.0230579 | + | 0.0230579i | −0.718542 | − | 0.695484i | \(-0.755190\pi\) |
0.695484 | + | 0.718542i | \(0.255190\pi\) | |||||||
\(594\) | − | 291767.i | − | 0.826920i | ||||||
\(595\) | −2937.17 | − | 4504.09i | −0.00829650 | − | 0.0127225i | ||||
\(596\) | 131473. | 0.370122 | ||||||||
\(597\) | 9486.35 | + | 9486.35i | 0.0266165 | + | 0.0266165i | ||||
\(598\) | −8675.63 | + | 8675.63i | −0.0242604 | + | 0.0242604i | ||||
\(599\) | 193242.i | 0.538578i | 0.963059 | + | 0.269289i | \(0.0867887\pi\) | ||||
−0.963059 | + | 0.269289i | \(0.913211\pi\) | |||||||
\(600\) | −81936.0 | − | 36107.8i | −0.227600 | − | 0.100299i | ||||
\(601\) | 6464.17 | 0.0178963 | 0.00894816 | − | 0.999960i | \(-0.497152\pi\) | ||||
0.00894816 | + | 0.999960i | \(0.497152\pi\) | |||||||
\(602\) | 42381.8 | + | 42381.8i | 0.116946 | + | 0.116946i | ||||
\(603\) | −62291.2 | + | 62291.2i | −0.171314 | + | 0.171314i | ||||
\(604\) | 202565.i | 0.555253i | ||||||||
\(605\) | −67408.4 | + | 43957.8i | −0.184163 | + | 0.120095i | ||||
\(606\) | −115226. | −0.313766 | ||||||||
\(607\) | 417558. | + | 417558.i | 1.13329 | + | 1.13329i | 0.989627 | + | 0.143658i | \(0.0458866\pi\) |
0.143658 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(608\) | 74488.3 | − | 74488.3i | 0.201503 | − | 0.201503i | ||||
\(609\) | 196317.i | 0.529325i | ||||||||
\(610\) | −350550. | − | 73816.0i | −0.942087 | − | 0.198377i | ||||
\(611\) | 5422.56 | 0.0145252 | ||||||||
\(612\) | 2283.34 | + | 2283.34i | 0.00609631 | + | 0.00609631i | ||||
\(613\) | 94239.1 | − | 94239.1i | 0.250790 | − | 0.250790i | −0.570505 | − | 0.821294i | \(-0.693252\pi\) |
0.821294 | + | 0.570505i | \(0.193252\pi\) | |||||||
\(614\) | 40207.5i | 0.106652i | ||||||||
\(615\) | 48946.5 | − | 232446.i | 0.129411 | − | 0.614570i | ||||
\(616\) | −65926.6 | −0.173740 | ||||||||
\(617\) | −408173. | − | 408173.i | −1.07220 | − | 1.07220i | −0.997182 | − | 0.0750142i | \(-0.976100\pi\) |
−0.0750142 | − | 0.997182i | \(-0.523900\pi\) | |||||||
\(618\) | 249386. | − | 249386.i | 0.652972 | − | 0.652972i | ||||
\(619\) | 402928.i | 1.05159i | 0.850611 | + | 0.525795i | \(0.176232\pi\) | ||||
−0.850611 | + | 0.525795i | \(0.823768\pi\) | |||||||
\(620\) | 12003.4 | + | 18406.9i | 0.0312262 | + | 0.0478847i | ||||
\(621\) | −85141.7 | −0.220780 | ||||||||
\(622\) | 171596. | + | 171596.i | 0.443534 | + | 0.443534i | ||||
\(623\) | −185345. | + | 185345.i | −0.477534 | + | 0.477534i | ||||
\(624\) | − | 15935.2i | − | 0.0409250i | ||||||
\(625\) | −263578. | − | 288296.i | −0.674759 | − | 0.738038i | ||||
\(626\) | 394035. | 1.00551 | ||||||||
\(627\) | −348179. | − | 348179.i | −0.885660 | − | 0.885660i | ||||
\(628\) | −154060. | + | 154060.i | −0.390635 | + | 0.390635i | ||||
\(629\) | − | 4852.11i | − | 0.0122639i | ||||||
\(630\) | 52831.5 | − | 34452.0i | 0.133110 | − | 0.0868028i | ||||
\(631\) | 495085. | 1.24343 | 0.621714 | − | 0.783244i | \(-0.286436\pi\) | ||||
0.621714 | + | 0.783244i | \(0.286436\pi\) | |||||||
\(632\) | −80162.4 | − | 80162.4i | −0.200695 | − | 0.200695i | ||||
\(633\) | −386853. | + | 386853.i | −0.965470 | + | 0.965470i | ||||
\(634\) | − | 384417.i | − | 0.956366i | ||||||
\(635\) | −280550. | − | 59075.8i | −0.695765 | − | 0.146508i | ||||
\(636\) | 176005. | 0.435122 | ||||||||
\(637\) | 53549.1 | + | 53549.1i | 0.131969 | + | 0.131969i | ||||
\(638\) | −380141. | + | 380141.i | −0.933905 | + | 0.933905i | ||||
\(639\) | − | 57175.6i | − | 0.140026i | ||||||
\(640\) | 7459.91 | − | 35427.0i | 0.0182127 | − | 0.0864916i | ||||
\(641\) | 130080. | 0.316588 | 0.158294 | − | 0.987392i | \(-0.449401\pi\) | ||||
0.158294 | + | 0.987392i | \(0.449401\pi\) | |||||||
\(642\) | −152454. | − | 152454.i | −0.369887 | − | 0.369887i | ||||
\(643\) | −83774.8 | + | 83774.8i | −0.202624 | + | 0.202624i | −0.801123 | − | 0.598499i | \(-0.795764\pi\) |
0.598499 | + | 0.801123i | \(0.295764\pi\) | |||||||
\(644\) | 19238.3i | 0.0463869i | ||||||||
\(645\) | 84038.6 | + | 128871.i | 0.202004 | + | 0.309768i | ||||
\(646\) | 16238.7 | 0.0389121 | ||||||||
\(647\) | 159581. | + | 159581.i | 0.381217 | + | 0.381217i | 0.871541 | − | 0.490323i | \(-0.163121\pi\) |
−0.490323 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(648\) | 25169.2 | − | 25169.2i | 0.0599403 | − | 0.0599403i | ||||
\(649\) | − | 511673.i | − | 1.21479i | ||||||
\(650\) | 28034.5 | − | 63615.9i | 0.0663537 | − | 0.150570i | ||||
\(651\) | 15166.3 | 0.0357864 | ||||||||
\(652\) | 189631. | + | 189631.i | 0.446081 | + | 0.446081i | ||||
\(653\) | 63954.6 | − | 63954.6i | 0.149984 | − | 0.149984i | −0.628127 | − | 0.778111i | \(-0.716178\pi\) |
0.778111 | + | 0.628127i | \(0.216178\pi\) | |||||||
\(654\) | 111876.i | 0.261567i | ||||||||
\(655\) | −636861. | + | 415305.i | −1.48444 | + | 0.968020i | ||||
\(656\) | 96047.2 | 0.223191 | ||||||||
\(657\) | 51652.5 | + | 51652.5i | 0.119663 | + | 0.119663i | ||||
\(658\) | 6012.30 | − | 6012.30i | 0.0138864 | − | 0.0138864i | ||||
\(659\) | − | 52015.9i | − | 0.119775i | −0.998205 | − | 0.0598873i | \(-0.980926\pi\) | ||
0.998205 | − | 0.0598873i | \(-0.0190741\pi\) | |||||||
\(660\) | −165595. | − | 34869.7i | −0.380154 | − | 0.0800497i | ||||
\(661\) | 386314. | 0.884173 | 0.442086 | − | 0.896972i | \(-0.354238\pi\) | ||||
0.442086 | + | 0.896972i | \(0.354238\pi\) | |||||||
\(662\) | 22898.0 | + | 22898.0i | 0.0522494 | + | 0.0522494i | ||||
\(663\) | 1736.96 | − | 1736.96i | 0.00395151 | − | 0.00395151i | ||||
\(664\) | − | 116439.i | − | 0.264097i | ||||||
\(665\) | 65355.5 | − | 310372.i | 0.147788 | − | 0.701841i | ||||
\(666\) | 56913.7 | 0.128312 | ||||||||
\(667\) | 110930. | + | 110930.i | 0.249344 | + | 0.249344i | ||||
\(668\) | −7260.63 | + | 7260.63i | −0.0162713 | + | 0.0162713i | ||||
\(669\) | 482799.i | 1.07873i | ||||||||
\(670\) | 83164.0 | + | 127530.i | 0.185262 | + | 0.284095i | ||||
\(671\) | −677060. | −1.50377 | ||||||||
\(672\) | −17668.3 | − | 17668.3i | −0.0391251 | − | 0.0391251i | ||||
\(673\) | 344390. | − | 344390.i | 0.760362 | − | 0.760362i | −0.216026 | − | 0.976388i | \(-0.569310\pi\) |
0.976388 | + | 0.216026i | \(0.0693095\pi\) | |||||||
\(674\) | − | 569281.i | − | 1.25316i | ||||||
\(675\) | 449723. | − | 174596.i | 0.987047 | − | 0.383201i | ||||
\(676\) | −216116. | −0.472926 | ||||||||
\(677\) | 265651. | + | 265651.i | 0.579608 | + | 0.579608i | 0.934795 | − | 0.355187i | \(-0.115583\pi\) |
−0.355187 | + | 0.934795i | \(0.615583\pi\) | |||||||
\(678\) | −50100.1 | + | 50100.1i | −0.108988 | + | 0.108988i | ||||
\(679\) | − | 27682.2i | − | 0.0600428i | ||||||
\(680\) | 4674.73 | − | 3048.45i | 0.0101097 | − | 0.00659266i | ||||
\(681\) | −520992. | −1.12341 | ||||||||
\(682\) | 29367.5 | + | 29367.5i | 0.0631390 | + | 0.0631390i | ||||
\(683\) | 292240. | − | 292240.i | 0.626467 | − | 0.626467i | −0.320710 | − | 0.947177i | \(-0.603922\pi\) |
0.947177 | + | 0.320710i | \(0.103922\pi\) | |||||||
\(684\) | 190474.i | 0.407121i | ||||||||
\(685\) | 91938.2 | + | 19359.6i | 0.195936 | + | 0.0412586i | ||||
\(686\) | 266801. | 0.566942 | ||||||||
\(687\) | 460137. | + | 460137.i | 0.974930 | + | 0.974930i | ||||
\(688\) | −43987.4 | + | 43987.4i | −0.0929291 | + | 0.0929291i | ||||
\(689\) | 136652.i | 0.287857i | ||||||||
\(690\) | −10175.5 | + | 48323.0i | −0.0213725 | + | 0.101498i | ||||
\(691\) | 231240. | 0.484292 | 0.242146 | − | 0.970240i | \(-0.422149\pi\) | ||||
0.242146 | + | 0.970240i | \(0.422149\pi\) | |||||||
\(692\) | 171509. | + | 171509.i | 0.358157 | + | 0.358157i | ||||
\(693\) | 84290.5 | − | 84290.5i | 0.175514 | − | 0.175514i | ||||
\(694\) | 27595.3i | 0.0572949i | ||||||||
\(695\) | −15305.2 | − | 23470.2i | −0.0316861 | − | 0.0485899i | ||||
\(696\) | −203754. | −0.420619 | ||||||||
\(697\) | 10469.3 | + | 10469.3i | 0.0215502 | + | 0.0215502i | ||||
\(698\) | −241163. | + | 241163.i | −0.494994 | + | 0.494994i | ||||
\(699\) | 71443.0i | 0.146219i | ||||||||
\(700\) | −39451.1 | − | 101618.i | −0.0805125 | − | 0.207383i | ||||
\(701\) | 238530. | 0.485407 | 0.242704 | − | 0.970101i | \(-0.421966\pi\) | ||||
0.242704 | + | 0.970101i | \(0.421966\pi\) | |||||||
\(702\) | 60710.0 | + | 60710.0i | 0.123193 | + | 0.123193i | ||||
\(703\) | 202380. | − | 202380.i | 0.409502 | − | 0.409502i | ||||
\(704\) | − | 68424.3i | − | 0.138059i | ||||||
\(705\) | 18281.8 | − | 11921.8i | 0.0367824 | − | 0.0239862i | ||||
\(706\) | −396559. | −0.795606 | ||||||||
\(707\) | −99192.4 | − | 99192.4i | −0.198445 | − | 0.198445i | ||||
\(708\) | 137128. | − | 137128.i | 0.273564 | − | 0.273564i | ||||
\(709\) | − | 360860.i | − | 0.717872i | −0.933362 | − | 0.358936i | \(-0.883140\pi\) | ||
0.933362 | − | 0.358936i | \(-0.116860\pi\) | |||||||
\(710\) | −96695.7 | − | 20361.4i | −0.191818 | − | 0.0403915i | ||||
\(711\) | 204983. | 0.405489 | ||||||||
\(712\) | −192367. | − | 192367.i | −0.379464 | − | 0.379464i | ||||
\(713\) | 8569.84 | − | 8569.84i | 0.0168575 | − | 0.0168575i | ||||
\(714\) | − | 3851.73i | − | 0.00755543i | ||||||
\(715\) | 27073.1 | − | 128570.i | 0.0529574 | − | 0.251494i | ||||
\(716\) | 166810. | 0.325384 | ||||||||
\(717\) | −121723. | − | 121723.i | −0.236774 | − | 0.236774i | ||||
\(718\) | 132294. | − | 132294.i | 0.256621 | − | 0.256621i | ||||
\(719\) | 687332.i | 1.32956i | 0.747038 | + | 0.664781i | \(0.231475\pi\) | ||||
−0.747038 | + | 0.664781i | \(0.768525\pi\) | |||||||
\(720\) | 35757.3 | + | 54833.0i | 0.0689762 | + | 0.105774i | ||||
\(721\) | 429367. | 0.825958 | ||||||||
\(722\) | 416666. | + | 416666.i | 0.799307 | + | 0.799307i | ||||
\(723\) | 418348. | − | 418348.i | 0.800316 | − | 0.800316i | ||||
\(724\) | − | 143935.i | − | 0.274593i | ||||||
\(725\) | −813420. | − | 358461.i | −1.54753 | − | 0.681970i | ||||
\(726\) | −57645.2 | −0.109368 | ||||||||
\(727\) | 77256.9 | + | 77256.9i | 0.146173 | + | 0.146173i | 0.776406 | − | 0.630233i | \(-0.217041\pi\) |
−0.630233 | + | 0.776406i | \(0.717041\pi\) | |||||||
\(728\) | 13717.8 | − | 13717.8i | 0.0258834 | − | 0.0258834i | ||||
\(729\) | 460213.i | 0.865972i | ||||||||
\(730\) | 105749. | − | 68960.5i | 0.198441 | − | 0.129406i | ||||
\(731\) | −9589.38 | −0.0179455 | ||||||||
\(732\) | −181451. | − | 181451.i | −0.338640 | − | 0.338640i | ||||
\(733\) | −377934. | + | 377934.i | −0.703409 | + | 0.703409i | −0.965141 | − | 0.261731i | \(-0.915707\pi\) |
0.261731 | + | 0.965141i | \(0.415707\pi\) | |||||||
\(734\) | 439911.i | 0.816531i | ||||||||
\(735\) | 298267. | + | 62806.6i | 0.552116 | + | 0.116260i | ||||
\(736\) | −19967.2 | −0.0368605 | ||||||||
\(737\) | 203470. | + | 203470.i | 0.374597 | + | 0.374597i | ||||
\(738\) | −122801. | + | 122801.i | −0.225470 | + | 0.225470i | ||||
\(739\) | − | 65835.1i | − | 0.120550i | −0.998182 | − | 0.0602752i | \(-0.980802\pi\) | ||
0.998182 | − | 0.0602752i | \(-0.0191978\pi\) | |||||||
\(740\) | 20268.1 | − | 96252.6i | 0.0370125 | − | 0.175772i | ||||
\(741\) | 144896. | 0.263888 | ||||||||
\(742\) | 151514. | + | 151514.i | 0.275197 | + | 0.275197i | ||||
\(743\) | −121704. | + | 121704.i | −0.220459 | + | 0.220459i | −0.808692 | − | 0.588233i | \(-0.799824\pi\) |
0.588233 | + | 0.808692i | \(0.299824\pi\) | |||||||
\(744\) | 15740.9i | 0.0284370i | ||||||||
\(745\) | 224421. | + | 344145.i | 0.404344 | + | 0.620053i | ||||
\(746\) | 250094. | 0.449393 | ||||||||
\(747\) | 148874. | + | 148874.i | 0.266794 | + | 0.266794i | ||||
\(748\) | 7458.35 | − | 7458.35i | 0.0133303 | − | 0.0133303i | ||||
\(749\) | − | 262480.i | − | 0.467878i | ||||||
\(750\) | −45346.4 | − | 276111.i | −0.0806158 | − | 0.490864i | ||||
\(751\) | 121197. | 0.214888 | 0.107444 | − | 0.994211i | \(-0.465733\pi\) | ||||
0.107444 | + | 0.994211i | \(0.465733\pi\) | |||||||
\(752\) | 6240.08 | + | 6240.08i | 0.0110345 | + | 0.0110345i | ||||
\(753\) | −388141. | + | 388141.i | −0.684541 | + | 0.684541i | ||||
\(754\) | − | 158197.i | − | 0.278263i | ||||||
\(755\) | −530236. | + | 345773.i | −0.930198 | + | 0.606593i | ||||
\(756\) | 134625. | 0.235550 | ||||||||
\(757\) | 547316. | + | 547316.i | 0.955095 | + | 0.955095i | 0.999034 | − | 0.0439395i | \(-0.0139909\pi\) |
−0.0439395 | + | 0.999034i | \(0.513991\pi\) | |||||||
\(758\) | 221211. | − | 221211.i | 0.385007 | − | 0.385007i | ||||
\(759\) | 93332.0i | 0.162012i | ||||||||
\(760\) | 322131. | + | 67831.6i | 0.557705 | + | 0.117437i | ||||
\(761\) | 652879. | 1.12736 | 0.563681 | − | 0.825992i | \(-0.309385\pi\) | ||||
0.563681 | + | 0.825992i | \(0.309385\pi\) | |||||||
\(762\) | −145218. | − | 145218.i | −0.250097 | − | 0.250097i | ||||
\(763\) | −96308.6 | + | 96308.6i | −0.165431 | + | 0.165431i | ||||
\(764\) | 284775.i | 0.487882i | ||||||||
\(765\) | −2079.28 | + | 9874.47i | −0.00355297 | + | 0.0168730i | ||||
\(766\) | 4738.14 | 0.00807515 | ||||||||
\(767\) | 106467. | + | 106467.i | 0.180978 | + | 0.180978i | ||||
\(768\) | 18337.6 | − | 18337.6i | 0.0310900 | − | 0.0310900i | ||||
\(769\) | 322701.i | 0.545692i | 0.962058 | + | 0.272846i | \(0.0879649\pi\) | ||||
−0.962058 | + | 0.272846i | \(0.912035\pi\) | |||||||
\(770\) | −112535. | − | 172570.i | −0.189804 | − | 0.291061i | ||||
\(771\) | −388349. | −0.653301 | ||||||||
\(772\) | −75419.8 | − | 75419.8i | −0.126547 | − | 0.126547i | ||||
\(773\) | −684980. | + | 684980.i | −1.14636 | + | 1.14636i | −0.159091 | + | 0.987264i | \(0.550856\pi\) |
−0.987264 | + | 0.159091i | \(0.949144\pi\) | |||||||
\(774\) | − | 112480.i | − | 0.187756i | ||||||
\(775\) | −27692.6 | + | 62840.1i | −0.0461063 | + | 0.104625i | ||||
\(776\) | 28731.0 | 0.0477119 | ||||||||
\(777\) | −48003.4 | − | 48003.4i | −0.0795116 | − | 0.0795116i | ||||
\(778\) | 91933.9 | − | 91933.9i | 0.151886 | − | 0.151886i | ||||
\(779\) | 873338.i | 1.43916i | ||||||||
\(780\) | 41712.1 | − | 27201.0i | 0.0685603 | − | 0.0447090i | ||||
\(781\) | −186760. | −0.306183 | ||||||||
\(782\) | −2176.45 | − | 2176.45i | −0.00355906 | − | 0.00355906i | ||||
\(783\) | 776264. | − | 776264.i | 1.26615 | − | 1.26615i | ||||
\(784\) | 123245.i | 0.200510i | ||||||||
\(785\) | −666247. | − | 140293.i | −1.08117 | − | 0.227665i | ||||
\(786\) | −544620. | −0.881553 | ||||||||
\(787\) | 455092. | + | 455092.i | 0.734768 | + | 0.734768i | 0.971560 | − | 0.236792i | \(-0.0760961\pi\) |
−0.236792 | + | 0.971560i | \(0.576096\pi\) | |||||||
\(788\) | 225866. | − | 225866.i | 0.363746 | − | 0.363746i | ||||
\(789\) | − | 171306.i | − | 0.275181i | ||||||
\(790\) | 72998.6 | − | 346669.i | 0.116966 | − | 0.555470i | ||||
\(791\) | −86257.3 | −0.137861 | ||||||||
\(792\) | 87484.0 | + | 87484.0i | 0.139469 | + | 0.139469i | ||||
\(793\) | 140881. | − | 140881.i | 0.224029 | − | 0.224029i | ||||
\(794\) | 636354.i | 1.00939i | ||||||||
\(795\) | 300436. | + | 460712.i | 0.475354 | + | 0.728946i | ||||
\(796\) | −16951.4 | −0.0267534 | ||||||||
\(797\) | 641033. | + | 641033.i | 1.00917 | + | 1.00917i | 0.999958 | + | 0.00921058i | \(0.00293186\pi\) |
0.00921058 | + | 0.999958i | \(0.497068\pi\) | |||||||
\(798\) | 160654. | − | 160654.i | 0.252282 | − | 0.252282i | ||||
\(799\) | 1360.35i | 0.00213088i | ||||||||
\(800\) | 105468. | − | 40945.8i | 0.164793 | − | 0.0639777i | ||||
\(801\) | 491902. | 0.766679 | ||||||||
\(802\) | −252289. | − | 252289.i | −0.392238 | − | 0.392238i | ||||
\(803\) | 168719. | − | 168719.i | 0.261657 | − | 0.261657i | ||||
\(804\) | 109059.i | 0.168714i | ||||||||
\(805\) | −50358.4 | + | 32839.3i | −0.0777105 | + | 0.0506760i | ||||
\(806\) | −12221.4 | −0.0188127 | ||||||||
\(807\) | 416452. | + | 416452.i | 0.639467 | + | 0.639467i | ||||
\(808\) | 102950. | − | 102950.i | 0.157690 | − | 0.157690i | ||||
\(809\) | 475560.i | 0.726621i | 0.931668 | + | 0.363311i | \(0.118354\pi\) | ||||
−0.931668 | + | 0.363311i | \(0.881646\pi\) | |||||||
\(810\) | 108846. | + | 22919.9i | 0.165899 | + | 0.0349335i | ||||
\(811\) | 555596. | 0.844729 | 0.422364 | − | 0.906426i | \(-0.361200\pi\) | ||||
0.422364 | + | 0.906426i | \(0.361200\pi\) | |||||||
\(812\) | −175402. | − | 175402.i | −0.266025 | − | 0.266025i | ||||
\(813\) | −372576. | + | 372576.i | −0.563682 | + | 0.563682i | ||||
\(814\) | − | 185904.i | − | 0.280569i | ||||||
\(815\) | −172684. | + | 820074.i | −0.259979 | + | 1.23463i | ||||
\(816\) | 3997.66 | 0.00600379 | ||||||||
\(817\) | −399969. | − | 399969.i | −0.599215 | − | 0.599215i | ||||
\(818\) | 295488. | − | 295488.i | 0.441604 | − | 0.441604i | ||||
\(819\) | 35077.8i | 0.0522956i | ||||||||
\(820\) | 163950. | + | 251414.i | 0.243828 | + | 0.373905i | ||||
\(821\) | −648338. | −0.961867 | −0.480934 | − | 0.876757i | \(-0.659702\pi\) | ||||
−0.480934 | + | 0.876757i | \(0.659702\pi\) | |||||||
\(822\) | 47588.9 | + | 47588.9i | 0.0704306 | + | 0.0704306i | ||||
\(823\) | −421156. | + | 421156.i | −0.621790 | + | 0.621790i | −0.945989 | − | 0.324199i | \(-0.894905\pi\) |
0.324199 | + | 0.945989i | \(0.394905\pi\) | |||||||
\(824\) | 445634.i | 0.656333i | ||||||||
\(825\) | −191392. | − | 492985.i | −0.281200 | − | 0.724312i | ||||
\(826\) | 236092. | 0.346036 | ||||||||
\(827\) | 231159. | + | 231159.i | 0.337986 | + | 0.337986i | 0.855609 | − | 0.517623i | \(-0.173183\pi\) |
−0.517623 | + | 0.855609i | \(0.673183\pi\) | |||||||
\(828\) | 25529.0 | − | 25529.0i | 0.0372369 | − | 0.0372369i | ||||
\(829\) | 1.21019e6i | 1.76095i | 0.474096 | + | 0.880473i | \(0.342775\pi\) | ||||
−0.474096 | + | 0.880473i | \(0.657225\pi\) | |||||||
\(830\) | 304793. | − | 198759.i | 0.442434 | − | 0.288516i | ||||
\(831\) | −607875. | −0.880262 | ||||||||
\(832\) | 14237.5 | + | 14237.5i | 0.0205678 | + | 0.0205678i | ||||
\(833\) | −13433.8 | + | 13433.8i | −0.0193602 | + | 0.0193602i | ||||
\(834\) | − | 20070.8i | − | 0.0288558i | ||||||
\(835\) | −31399.2 | − | 6611.78i | −0.0450345 | − | 0.00948299i | ||||
\(836\) | 622169. | 0.890217 | ||||||||
\(837\) | −59969.7 | − | 59969.7i | −0.0856014 | − | 0.0856014i | ||||
\(838\) | 407247. | − | 407247.i | 0.579923 | − | 0.579923i | ||||
\(839\) | 286832.i | 0.407477i | 0.979025 | + | 0.203739i | \(0.0653093\pi\) | ||||
−0.979025 | + | 0.203739i | \(0.934691\pi\) | |||||||
\(840\) | 16089.3 | − | 76407.8i | 0.0228023 | − | 0.108288i | ||||
\(841\) | −1.31549e6 | −1.85993 | ||||||||
\(842\) | 227730. | + | 227730.i | 0.321215 | + | 0.321215i | ||||
\(843\) | 169117. | − | 169117.i | 0.237975 | − | 0.237975i | ||||
\(844\) | − | 691278.i | − | 0.970439i | ||||||
\(845\) | −368904. | − | 565706.i | −0.516654 | − | 0.792278i | ||||
\(846\) | −15956.5 | −0.0222945 | ||||||||
\(847\) | −49623.8 | − | 49623.8i | −0.0691708 | − | 0.0691708i | ||||
\(848\) | −157254. | + | 157254.i | −0.218680 | + | 0.218680i | ||||
\(849\) | − | 172845.i | − | 0.239796i | ||||||
\(850\) | 15959.3 | + | 7032.99i | 0.0220890 | + | 0.00973424i | ||||
\(851\) | −54249.4 | −0.0749094 | ||||||||
\(852\) | −50051.4 | − | 50051.4i | −0.0689505 | − | 0.0689505i | ||||
\(853\) | 648590. | − | 648590.i | 0.891399 | − | 0.891399i | −0.103256 | − | 0.994655i | \(-0.532926\pi\) |
0.994655 | + | 0.103256i | \(0.0329261\pi\) | |||||||
\(854\) | − | 312404.i | − | 0.428352i | ||||||
\(855\) | −498586. | + | 325134.i | −0.682037 | + | 0.444765i | ||||
\(856\) | 272424. | 0.371790 | ||||||||
\(857\) | 220314. | + | 220314.i | 0.299972 | + | 0.299972i | 0.841003 | − | 0.541031i | \(-0.181966\pi\) |
−0.541031 | + | 0.841003i | \(0.681966\pi\) | |||||||
\(858\) | 66550.0 | − | 66550.0i | 0.0904011 | − | 0.0904011i | ||||
\(859\) | 52637.7i | 0.0713363i | 0.999364 | + | 0.0356682i | \(0.0113559\pi\) | ||||
−0.999364 | + | 0.0356682i | \(0.988644\pi\) | |||||||
\(860\) | −190227. | − | 40056.4i | −0.257203 | − | 0.0541596i | ||||
\(861\) | 207152. | 0.279436 | ||||||||
\(862\) | 620739. | + | 620739.i | 0.835400 | + | 0.835400i | ||||
\(863\) | 949999. | − | 949999.i | 1.27556 | − | 1.27556i | 0.332435 | − | 0.943126i | \(-0.392130\pi\) |
0.943126 | − | 0.332435i | \(-0.107870\pi\) | |||||||
\(864\) | 139725.i | 0.187175i | ||||||||
\(865\) | −156182. | + | 741703.i | −0.208736 | + | 0.991283i | ||||
\(866\) | 544654. | 0.726248 | ||||||||
\(867\) | −373485. | − | 373485.i | −0.496861 | − | 0.496861i | ||||
\(868\) | −13550.5 | + | 13550.5i | −0.0179853 | + | 0.0179853i | ||||
\(869\) | − | 669563.i | − | 0.886649i | ||||||
\(870\) | −347803. | − | 533349.i | −0.459510 | − | 0.704649i | ||||
\(871\) | −84674.6 | −0.111614 | ||||||||
\(872\) | −99957.4 | − | 99957.4i | −0.131456 | − | 0.131456i | ||||
\(873\) | −36734.0 | + | 36734.0i | −0.0481992 | + | 0.0481992i | ||||
\(874\) | − | 181558.i | − | 0.237680i | ||||||
\(875\) | 198654. | − | 276726.i | 0.259466 | − | 0.361439i | ||||
\(876\) | 90433.0 | 0.117847 | ||||||||
\(877\) | −534065. | − | 534065.i | −0.694376 | − | 0.694376i | 0.268816 | − | 0.963192i | \(-0.413368\pi\) |
−0.963192 | + | 0.268816i | \(0.913368\pi\) | |||||||
\(878\) | −594889. | + | 594889.i | −0.771697 | + | 0.771697i | ||||
\(879\) | 254867.i | 0.329865i | ||||||||
\(880\) | 179108. | − | 116798.i | 0.231286 | − | 0.150825i | ||||
\(881\) | −1.00777e6 | −1.29841 | −0.649204 | − | 0.760614i | \(-0.724898\pi\) | ||||
−0.649204 | + | 0.760614i | \(0.724898\pi\) | |||||||
\(882\) | −157574. | − | 157574.i | −0.202558 | − | 0.202558i | ||||
\(883\) | 522706. | − | 522706.i | 0.670403 | − | 0.670403i | −0.287406 | − | 0.957809i | \(-0.592793\pi\) |
0.957809 | + | 0.287406i | \(0.0927929\pi\) | |||||||
\(884\) | 3103.82i | 0.00397184i | ||||||||
\(885\) | 593020. | + | 124873.i | 0.757151 | + | 0.159435i | ||||
\(886\) | −787774. | −1.00354 | ||||||||
\(887\) | −511630. | − | 511630.i | −0.650292 | − | 0.650292i | 0.302771 | − | 0.953063i | \(-0.402088\pi\) |
−0.953063 | + | 0.302771i | \(0.902088\pi\) | |||||||
\(888\) | 49822.1 | − | 49822.1i | 0.0631824 | − | 0.0631824i | ||||
\(889\) | − | 250021.i | − | 0.316353i | ||||||
\(890\) | 175176. | − | 831906.i | 0.221154 | − | 1.05025i | ||||
\(891\) | 210227. | 0.264810 | ||||||||
\(892\) | −431363. | − | 431363.i | −0.542142 | − | 0.542142i | ||||
\(893\) | −56739.8 | + | 56739.8i | −0.0711517 | + | 0.0711517i | ||||
\(894\) | 294300.i | 0.368227i | ||||||||
\(895\) | 284740. | + | 436643.i | 0.355470 | + | 0.545105i | ||||
\(896\) | 31571.9 | 0.0393264 | ||||||||
\(897\) | −19420.2 | − | 19420.2i | −0.0241362 | − | 0.0241362i | ||||
\(898\) | −555157. | + | 555157.i | −0.688435 | + | 0.688435i | ||||
\(899\) | 156268.i | 0.193353i | ||||||||
\(900\) | −82494.6 | + | 187197.i | −0.101845 | + | 0.231107i | ||||
\(901\) | −34281.8 | −0.0422293 | ||||||||
\(902\) | 401121. | + | 401121.i | 0.493017 | + | 0.493017i | ||||
\(903\) | −94870.8 | + | 94870.8i | −0.116347 | + | 0.116347i | ||||
\(904\) | − | 89525.3i | − | 0.109549i | ||||||
\(905\) | 376765. | − | 245693.i | 0.460016 | − | 0.299982i | ||||
\(906\) | −453438. | −0.552410 | ||||||||
\(907\) | 784298. | + | 784298.i | 0.953382 | + | 0.953382i | 0.998961 | − | 0.0455791i | \(-0.0145133\pi\) |
−0.0455791 | + | 0.998961i | \(0.514513\pi\) | |||||||
\(908\) | 465487. | − | 465487.i | 0.564594 | − | 0.564594i | ||||
\(909\) | 263255.i | 0.318602i | ||||||||
\(910\) | 59323.8 | + | 12491.9i | 0.0716384 | + | 0.0150850i | ||||
\(911\) | −1.57547e6 | −1.89834 | −0.949171 | − | 0.314762i | \(-0.898075\pi\) | ||||
−0.949171 | + | 0.314762i | \(0.898075\pi\) | |||||||
\(912\) | 166741. | + | 166741.i | 0.200471 | + | 0.200471i | ||||
\(913\) | 486285. | − | 486285.i | 0.583377 | − | 0.583377i | ||||
\(914\) | − | 819964.i | − | 0.981527i | ||||||
\(915\) | 165236. | − | 784701.i | 0.197361 | − | 0.937264i | ||||
\(916\) | −822230. | −0.979947 | ||||||||
\(917\) | −468836. | − | 468836.i | −0.557548 | − | 0.557548i | ||||
\(918\) | −15230.3 | + | 15230.3i | −0.0180727 | + | 0.0180727i | ||||
\(919\) | 575240.i | 0.681111i | 0.940224 | + | 0.340556i | \(0.110615\pi\) | ||||
−0.940224 | + | 0.340556i | \(0.889385\pi\) | |||||||
\(920\) | −34083.4 | − | 52266.2i | −0.0402687 | − | 0.0617512i | ||||
\(921\) | −90003.6 | −0.106106 | ||||||||
\(922\) | 6199.71 | + | 6199.71i | 0.00729306 | + | 0.00729306i | ||||
\(923\) | 38860.4 | − | 38860.4i | 0.0456146 | − | 0.0456146i | ||||
\(924\) | − | 147576.i | − | 0.172850i | ||||||
\(925\) | 286549. | − | 111247.i | 0.334900 | − | 0.130018i | ||||
\(926\) | −249015. | −0.290405 | ||||||||
\(927\) | −569766. | − | 569766.i | −0.663036 | − | 0.663036i | ||||
\(928\) | 182047. | − | 182047.i | 0.211392 | − | 0.211392i | ||||
\(929\) | − | 1.41732e6i | − | 1.64225i | −0.570752 | − | 0.821123i | \(-0.693348\pi\) | ||
0.570752 | − | 0.821123i | \(-0.306652\pi\) | |||||||
\(930\) | −41203.5 | + | 26869.3i | −0.0476396 | + | 0.0310663i | ||||
\(931\) | −1.12064e6 | −1.29290 | ||||||||
\(932\) | −63831.7 | − | 63831.7i | −0.0734859 | − | 0.0734859i | ||||
\(933\) | −384115. | + | 384115.i | −0.441263 | + | 0.441263i | ||||
\(934\) | − | 747603.i | − | 0.856993i | ||||||
\(935\) | 32254.2 | + | 6791.83i | 0.0368947 | + | 0.00776897i | ||||
\(936\) | −36406.8 | −0.0415557 | ||||||||
\(937\) | −1.10376e6 | − | 1.10376e6i | −1.25717 | − | 1.25717i | −0.952437 | − | 0.304735i | \(-0.901432\pi\) |
−0.304735 | − | 0.952437i | \(-0.598568\pi\) | |||||||
\(938\) | −93883.5 | + | 93883.5i | −0.106705 | + | 0.106705i | ||||
\(939\) | 882040.i | 1.00036i | ||||||||
\(940\) | −5682.43 | + | 26985.7i | −0.00643100 | + | 0.0305407i | ||||
\(941\) | 305672. | 0.345205 | 0.172602 | − | 0.984992i | \(-0.444782\pi\) | ||||
0.172602 | + | 0.984992i | \(0.444782\pi\) | |||||||
\(942\) | −344861. | − | 344861.i | −0.388636 | − | 0.388636i | ||||
\(943\) | 117053. | − | 117053.i | 0.131631 | − | 0.131631i | ||||
\(944\) | 245037.i | 0.274971i | ||||||||
\(945\) | 229801. | + | 352396.i | 0.257329 | + | 0.394609i | ||||
\(946\) | −367408. | −0.410551 | ||||||||
\(947\) | 377220. | + | 377220.i | 0.420624 | + | 0.420624i | 0.885419 | − | 0.464794i | \(-0.153872\pi\) |
−0.464794 | + | 0.885419i | \(0.653872\pi\) | |||||||
\(948\) | 179442. | − | 179442.i | 0.199667 | − | 0.199667i | ||||
\(949\) | 70213.0i | 0.0779624i | ||||||||
\(950\) | 372312. | + | 958998.i | 0.412534 | + | 1.06260i | ||||
\(951\) | 860510. | 0.951470 | ||||||||
\(952\) | 3441.38 | + | 3441.38i | 0.00379716 | + | 0.00379716i | ||||
\(953\) | −349391. | + | 349391.i | −0.384703 | + | 0.384703i | −0.872793 | − | 0.488090i | \(-0.837694\pi\) |
0.488090 | + | 0.872793i | \(0.337694\pi\) | |||||||
\(954\) | − | 402114.i | − | 0.441828i | ||||||
\(955\) | −745429. | + | 486103.i | −0.817334 | + | 0.532993i | ||||
\(956\) | 217510. | 0.237992 | ||||||||
\(957\) | −850937. | − | 850937.i | −0.929124 | − | 0.929124i | ||||
\(958\) | −167956. | + | 167956.i | −0.183006 | + | 0.183006i | ||||
\(959\) | 81933.6i | 0.0890892i | ||||||||
\(960\) | 79302.6 | + | 16698.9i | 0.0860488 | + | 0.0181194i | ||||
\(961\) | −911449. | −0.986928 | ||||||||
\(962\) | 38682.4 | + | 38682.4i | 0.0417987 | + | 0.0417987i | ||||
\(963\) | −348308. | + | 348308.i | −0.375587 | + | 0.375587i | ||||
\(964\) | 747558.i | 0.804434i | ||||||||
\(965\) | 68679.9 | − | 326159.i | 0.0737522 | − | 0.350247i | ||||
\(966\) | −43064.6 | −0.0461494 | ||||||||
\(967\) | 103657. | + | 103657.i | 0.110853 | + | 0.110853i | 0.760358 | − | 0.649505i | \(-0.225024\pi\) |
−0.649505 | + | 0.760358i | \(0.725024\pi\) | |||||||
\(968\) | 51503.8 | − | 51503.8i | 0.0549653 | − | 0.0549653i | ||||
\(969\) | 36349.9i | 0.0387129i | ||||||||
\(970\) | 49043.0 | + | 75206.4i | 0.0521235 | + | 0.0799302i | ||||
\(971\) | −119158. | −0.126381 | −0.0631907 | − | 0.998001i | \(-0.520128\pi\) | ||||
−0.0631907 | + | 0.998001i | \(0.520128\pi\) | |||||||
\(972\) | −297339. | − | 297339.i | −0.314717 | − | 0.314717i | ||||
\(973\) | 17277.9 | − | 17277.9i | 0.0182501 | − | 0.0182501i | ||||
\(974\) | 958443.i | 1.01030i | ||||||||
\(975\) | 142403. | + | 62754.6i | 0.149799 | + | 0.0660140i | ||||
\(976\) | 324240. | 0.340382 | ||||||||
\(977\) | −747694. | − | 747694.i | −0.783312 | − | 0.783312i | 0.197076 | − | 0.980388i | \(-0.436855\pi\) |
−0.980388 | + | 0.197076i | \(0.936855\pi\) | |||||||
\(978\) | −424485. | + | 424485.i | −0.443797 | + | 0.443797i | ||||
\(979\) | − | 1.60676e6i | − | 1.67643i | ||||||
\(980\) | −322606. | + | 210375.i | −0.335908 | + | 0.219050i | ||||
\(981\) | 255601. | 0.265598 | ||||||||
\(982\) | −117624. | − | 117624.i | −0.121976 | − | 0.121976i | ||||
\(983\) | 477597. | − | 477597.i | 0.494259 | − | 0.494259i | −0.415386 | − | 0.909645i | \(-0.636353\pi\) |
0.909645 | + | 0.415386i | \(0.136353\pi\) | |||||||
\(984\) | 215000.i | 0.222048i | ||||||||
\(985\) | 976776. | + | 205681.i | 1.00675 | + | 0.211993i | ||||
\(986\) | 39686.8 | 0.0408218 | ||||||||
\(987\) | 13458.4 | + | 13458.4i | 0.0138153 | + | 0.0138153i | ||||
\(988\) | −129459. | + | 129459.i | −0.132623 | + | 0.132623i | ||||
\(989\) | 107215.i | 0.109613i | ||||||||
\(990\) | −79665.9 | + | 378331.i | −0.0812834 | + | 0.386013i | ||||
\(991\) | 552759. | 0.562844 | 0.281422 | − | 0.959584i | \(-0.409194\pi\) | ||||
0.281422 | + | 0.959584i | \(0.409194\pi\) | |||||||
\(992\) | −14063.9 | − | 14063.9i | −0.0142917 | − | 0.0142917i | ||||
\(993\) | −51256.7 | + | 51256.7i | −0.0519819 | + | 0.0519819i | ||||
\(994\) | − | 86173.5i | − | 0.0872169i | ||||||
\(995\) | −28935.6 | − | 44372.1i | −0.0292271 | − | 0.0448192i | ||||
\(996\) | 260647. | 0.262745 | ||||||||
\(997\) | −187575. | − | 187575.i | −0.188705 | − | 0.188705i | 0.606431 | − | 0.795136i | \(-0.292601\pi\) |
−0.795136 | + | 0.606431i | \(0.792601\pi\) | |||||||
\(998\) | 347351. | − | 347351.i | 0.348745 | − | 0.348745i | ||||
\(999\) | 379624.i | 0.380385i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 230.5.f.a.47.15 | ✓ | 44 | |
5.3 | odd | 4 | inner | 230.5.f.a.93.15 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.5.f.a.47.15 | ✓ | 44 | 1.1 | even | 1 | trivial | |
230.5.f.a.93.15 | yes | 44 | 5.3 | odd | 4 | inner |